INQUIRY PHYSICS
A Modified Learning Cycle Curriculum
by Granger Meador
Unit 4: Projectiles
Student Papers
©2010 by Granger Meador
inquiryphysics.org
4 Projectile Motion
Nam e
Reading: GALILEO EXPLAINS PROJECTILE MOTION
In this investigation, you have studied the phenomenon of projectile motion. Perhaps you found it rather difficult
to deal with the fact that an object projected into space has two simultaneous motions - each totally independent
of the other. Indeed the idea of constant velocity and constant acceleration being present in the same object
at the same time is paradoxical. If it makes you feel any better, you are not alone in your confusion.
In fact, people of great wisdom denied the simultaneous motions of a projectile for many centuries.
In the sixteenth century it was reasoned that an object fired from a cannon had two distinct motions.
First, the object would have motion resulting from the explosion of the gunpowder, then it would fall
Figure 1
to the ground due to its natural motion. In other words, the cannonball would move in the direction
it was fired until the gunpowder's effect was gone, then it would fall straight to the earth. The path
would look something like Figure 1.
But, Galileo, a great sixteenth century physicist, proposed a quite different
hypothesis. He determined that the force of the gunpowder was applied
only at the instant of the explosion; the result of that force was the constant
velocity of the ball. As soon as the ball left the cannon, the force of gravity
began to cause the ball to accelerate toward the earth at a constant rate. He
proposed that the path of the ball would look like Figure 2.
The actual path follows a curve called a parabola. If you carefully watched
how balls were thrown during the lecture about two-dimensional motion,
you will have seen this yourself.
Figure 2
So, now that you are convinced that objects
moving through space follow curved parabolic paths due to the simultaneous presence of constant
horizontal velocity and constant vertical acceleration, what good is this knowledge? W ell, we've
already mentioned one important use (although not an altogether pleasant one) - the firing of
projectiles of war. Like the ancient catapults and cannons, modern artillery and bombs must be aimed
with the ultimate path of the object in mind. You can determine the horizontal distance covered by
a fired object and predict its vertical motion using the knowledge of vectors you gained in
investigation 2.
Another interesting consequence of the simultaneous motions of bodies in flight had much historical significance. Think - if you
drop a coin from the top of a tall ladder, where would it land? Better yet, if you dived from a diving board into a swimming pool
situated on a moving ship, would you land in the pool or on the deck of the ship? How silly, you say! The coin would drop at
the base of the ladder and you would land in the pool. But, now consider that the earth is moving at all times. So, the free-falling
coin leaves your hand while the ladder is in one place and lands on the ground after the ladder has moved a bit due to the motion
of the earth. Likewise, you dive from the diving board when the pool is in one position and land after the boat has moved due
to its own power as well as the motion of the earth. W ell now, are you still sure of your initial response?
Aristotle, a scientist of ancient Greece, and Galileo differed in their ideas
concerning this issue as well as the motion of falling bodies. Aristotle used this
very issue as evidence that the earth did not move. If the earth had motion of
its own, he reasoned, then an object dropped from the mast of a ship would fall
into the sea because the ship would move out from under the object. (He never
tested this, by the way.) If Aristotle had been right, you would not want to
practice your diving on a moving ship!
On the other hand, Galileo argued that an object dropped from the top of a ship's mast would land at the base of the mast because,
while the object was falling vertically, it also participated in the horizontal motion of the ship and earth. Thus, a falling object
had vertical motion due to the effect of gravity and also retained any horizontal motion initially given to it. This eventually led
to the concept of inertia which we will later study in greater detail.
Unit 4: Projectiles, Readings: Galileo Explains Projectile Motion and Trajectories
© 2010 by G. Meador – www.inquiryphysics.org
Reading: TRAJECTORIES
You have learned that any object that is projected by some means and continues in motion (free-fall) is a projectile. Falling bodies
are a special case of projectile motion. Projectile motion can also occur in two dimensions: the projectile can move both
horizontally and vertically. You have also learned that the horizontal and vertical motions of a projectile are independent.
Another important aspect of projectile motion is the path, or
trajectory of the object. The trajectory of a projectile is
curved; it is parabolic. This curved path is due to the object's
constant horizontal velocity and its changing vertical velocity.
Figure 3 shows vectors representing both horizontal and
vertical components (or parts) of velocity for a projectile
following a parabolic trajectory.
Figure 3
Notice that the horizontal component is always the same, and only
the vertical component changes. Note also that the actual or total
velocity is represented by the resultant vector of the horizontal and
vertical components. In other words, the actual velocity can be
found by vector addition of the horizontal and vertical portions of
that velocity. At the top of the arc the vertical component vanishes
to zero (v f vertically is zero). This means that the actual velocity at
that point is the horizontal velocity alone. Everywhere else the
magnitude of velocity is greater.
Figure 4 shows the trajectory of a projectile with the same launching
speed at a steeper angle. Notice that the initial velocity vector has
a greater vertical component than when the projection angle is less.
This greater component results in a higher path. But the horizontal
component is less so the range (horizontal distance) is less.
Figure 4
Figure 5 shows the trajectories of several projectiles all
having the same initial speed but different projection angles.
The figure neglects the effects of air resistance, so the paths
are all parabolas. Notice that these projectiles reach different
altitudes and have different ranges.
Note how maximum range is attained at an angle of 45E. This
holds true for such sports as baseball — the ball travels
farthest if it is batted at 45E. (This does not work when the
projectile is similar in weight to the force applied to it. Then
the best range is achieved at angles much less than 45E.)
It is interesting to note that two different angles can result in
the same range when they are equally offset from 45E
– compare 60E to 30E and also 75E to 15E.
Unit 4: Projectiles, Readings: Galileo Explains Projectile Motion and Trajectories
Figure 5
© 2010 by G. Meador – www.inquiryphysics.org
4 Projectile Motion
Nam e
W orksheet A: Applying the Readings
W rite the letter corresponding to the best answ er in the blank at the left of each question.
1.
W hich of the following would NOT be considered a projectile?
a. A cannonball fired towards a distant castle.
b. A cannonball rolling down a slope.
c. A cannonball fired straight outward from a castle wall.
d. A cannonball after it rolls off the edge of a cliff.
2.
The
a.
b.
c.
3.
In the absence of air friction, which component of a projectile's velocity will not change as the projectile
moves?
a. vertical
b. horizontal
c. both vertical and horizontal
4.
At the instant a ball is thrown horizontally with a large force, an identical ball is dropped from the same height.
W hich ball hits the ground first?
a. the projected ball
b. the dropped ball
c. neither - they hit simultaneously
5.
A ball is thrown up and forward into the air. At the very top of the ball's trajectory, its actual velocity is...
a. entirely vertical.
b. entirely horizontal.
c. both vertical and horizontal.
d. zero.
6.
In the absence of air resistance, the angle at which a projectile will go the farthest is...
a. 75E
b. 60E
c. 45E
d. 30E
7.
A ball thrown in the air will never go as far as physics ideally would predict because...
a. one can never throw the ball fast enough.
b. gravity is acting.
c. ideally the ball would never land.
d. air friction slows the ball.
8.
At
a.
b.
c.
d.
9.
A cannonball is launched from the ground at an angle of 30 degrees and a speed of 20 m/s. Ideally (no air
resistance) the ball will land on the ground with a speed of...
a. 40 m/s
b. 20 m/s
c. 10 m/s
d. 0 m/s
10.
A bullet fired horizontally hits the ground in 0.5 second. If it had been fired with a much higher speed in the
same direction, it would have hit the ground (neglecting the Earth's curvature and air resistance) in...
a. less than 0.5 s
b. more than 0.5 s
c. 0.5 s
horizontal component of a projectile's velocity is independent of...
the vertical component of its velocity.
the range of the projectile.
time.
what part of a trajectory does an upwardly hurled projectile have minimum speed?
W hen it is first projected.
Half-way to the top.
At the top of its trajectory.
W hen it returns to the ground.
Unit 4: Projectiles, Worksheet A: Applying the Readings
© 2010 by G. Meador – www.inquiryphysics.org
16.
11.
A projectile is fired horizontally above the surface of the moon (which has no atmosphere). The projectile
maintains its horizontal component of speed. This is because the object...
a. is not acted upon by any forces after it is fired.
b. is not acted on by horizontal forces after it is fired.
c. has no vertical speed to begin with.
d. is not acted upon by gravity.
12.
An object is dropped and falls freely to the ground with an acceleration of 1 g (1 g = 9.8 m/s 2). If it is thrown
upward at an angle instead, its free-fall acceleration would be...
a. 0 g
b. 1 g downward
c. 1 g upward
d. larger than 1 g
13.
A ball is hurled into the air at an angle of 30 degrees and lands on a target that is at the same level as that where
the ball started. The ball will also land on the target if it is thrown at an angle of...
a. 40 degrees
b. 45 degrees
c. 55 degrees
d. 60 degrees
14.
A rifle with a muzzle velocity of 100 m/s is fired horizontally from a tower. Neglecting air resistance, where
will the bullet be 1.00 second later?
a. 50.0 m downrange b. 98.0 m downrange
c. 100. m downrange d. 490 m downrange
15.
After a rock that is thrown straight up reaches the top of its path and is starting to fall back down, its
acceleration is (neglecting air resistance)...
a. greater than when it was at the top of its trajectory.
b. less than when it was at the top of its trajectory.
c. the same as when it was at the top of its trajectory.
Suppose that you are an accident
investigator and you are asked to
determine whether or not the car was
speeding before it crashed through the rail
of the bridge and into the mudbank, as
shown. The speed limit at the bridge is
50. mph or roughly 22 m/s. W hat is your
conclusion? Show your work.
Unit 4: Projectiles, Worksheet A: Applying the Readings
© 2010 by G. Meador – www.inquiryphysics.org
4 Projectile Motion
W orksheet B: W hen Projectiles Strike
Nam e
Trig-Based
Assum e air resistance is negligible and that g = S9.80 m /s2 (or S32.2 ft/s2 ). Show your work on this paper.
W ork m etric problem s in m eters and seconds and U.S. Custom ary System problem s in feet and seconds.
1.
An object, projected upward at an angle of 30.0E with the horizontal, has an initial speed of 128 ft/s.
a) In how many seconds will it reach the ground?
b) How far from the point of projection will it strike?
441 feet
c) Find the angle it strikes the ground at using
2.
A ball is thrown from the top of one building toward a tall building 50.0 feet away. The initial velocity of
the ball is 20.0 ft/s at 40.0E above the horizontal. How far above or below its original level will the ball
strike the opposite wall?
130 feet below
Unit 4: Projectiles, Worksheet B: When Projectiles Strike
©2010 by G. Meador – www.inquiryphysics.org
3.
A projectile is fired upward from the top edge of a vertical 200 meter cliff above a valley. Its initial velocity
is 60.0 m/s at 60.0E above the horizontal. Calculate the distance from the base of the cliff to the impact
point on the valley floor.
408 meters
4.
A plane with a speed of 105 m/s, diving at an angle of 60.0E with the vertical, releases a projectile at an
altitude of 875 m. How far does the projectile travel horizontally before striking the ground below?
5.
A marble with a speed of 15.0 cm/s rolls off the edge of a table 65.0 cm high. How far, horizontally, from
the table edge does the marble strike the floor?
Unit 4: Projectiles, Worksheet B: When Projectiles Strike
©2010 by G. Meador – www.inquiryphysics.org
4 Projectile Motion
Nam e
W orksheet C: Projectiles Strike Again
Trig-Based
Assum e air resistance is negligible and that g = S9.80 m /s2 (or S32.2 ft/s2 ). Show your work on this paper.
1.
A body projected upward from level ground at an angle of 20.0E with the horizontal has an initial speed of
30.0 m/s. How far from the starting point will it strike?
2.
An object is projected downward at an angle of 20.0E with the horizontal with an initial speed of 40.0 m/s
from the top of a cliff 150 m high.
a) In what time will it strike the ground?
b) How far from the foot of the cliff will it strike the ground?
c) At what angle with the horizontal will it strike?
U SE TRIG ON OM ETRY IN VO LVIN G TH E FIN AL VELOCITY VECTOR
3.
A rifle is aimed horizontally at a target 30.0 m away. The bullet hits the target 7.50 cm below the aiming
point. W hat is the muzzle velocity of the rifle?
Unit 4: Projectiles, Worksheet C: Projectiles Strike Again
©2010 by G. Meador – www.inquiryphysics.org
4.
A cannon on a level plain shoots a shell with a muzzle velocity of 60.0 m/s at 50.0E above the horizontal
toward a vertical cliff 365 m away. How far above the bottom does the shell strike the side wall of the cliff?
5.
A catapult hurls a stone at a speed of 65.0 m/s at an
angle of 37.0E above the horizontal. On the
downward part of its trajectory, it strikes a castle
wall 75.0 m above the level of the catapult. W hat
is the horizontal distance between the catapult and
the castle?
“I think we should change our attack strategy.”
6.
A batter hits a home run at W rigley Field. The ball leaves the bat with a velocity of 37.0 m/s at an angle
of 40.0E above the horizontal. A fielder who has a reach of 2.00 m above the ground is backed up against
the bleacher wall, which at W rigley Field is 118 m from home plate. The ball was 1.00 m above the ground
when it was hit. How high above the fielder's glove does the ball pass?
Unit 4: Projectiles, Worksheet C: Projectiles Strike Again
©2010 by G. Meador – www.inquiryphysics.org
INQUIRY PHYSICS TEST REVIEW
Units 1-4: One and Two-dimensional Motion
Name
(Non-Trig)
M ultiple Choice
Covers all topics: 1-d m otion, vectors, falling bodies, projectiles. Be prepared to m ake or interpret distance
or speed graphs of objects for ANY of the m otions we have studied, including falling objects and projectiles.
Know your rules of vector addition.
TO PREPARE:
Carefully review all of your notes and review the readings on projectiles. Study the m ultiple choice questions
on the m easurem ent and m otion and vectors quizzes, the projectiles reading worksheet, and do the
accom panying review concept questions.
Problems
Be prepared for a projectile problem , a falling body problem , a vector problem , and two 1-d problem s with one
having m ultiple steps (where you cannot solve for the answer directly, but m ust first find another given).
TO PREPARE:
Do the accom panying review problem s.
Inquiry Investigations 1-4 Test Review Assignment
Show your w ork on all problems, including givens, equations, and all appropriate units. Answ ers
should be expressed w ith the proper number of significant figures. Assume g = - 9.80 m/s 2 and that
air resistance is negligible.
1.
A stone is thrown straight downward with an initial speed of 8.00 m/s from a height of 25.0 meters.
a) Find the time it takes to reach the ground.
b)
2.
Find its impact velocity.
A supersonic airplane was flying horizontally with a speed of 620 m/s when a radar pod fell off. If the pod
travelled a horizontal distance of 40,300 m before it struck the ground, what was the altitude of the airplane?
20,700 m
Unit 1-4: One and Two-Dimensional Motion, Non-Trig Review I
©2010 by G. Meador – www.inquiryphysics.org
Inquiry Physics Unit 1-4 Test Review
Page 2
3.
How long does it take a car to travel 50.0 m while slowing from 20.0 m/s to a stop?
4.
A stone is shot upward with a speed of 20.0 m/s from a tower that is 45.0 m high, and strikes the ground at the
tower’s base. Find the impact speed of the stone.
5.
The Denver Casa Bonita restaurant features cliff divers. A diver launched horizontally from the 9.00 m tall
cliff at approximately 1.20 m/s. How far away from the base of the cliff was the diver when she hit the water?
6.
Phluffy the cat decides to swim across a river. The cat paddles due east at 5.0 m/s, and the river has a current
of 2.0 m/s due south. Find the magnitude and direction of Phluffy's resultant velocity (in m/s) by drawing a
scale diagram.
5.4 m/s at 22E S of E
Scale:
1 cm =
m/s
Resultant magnitude:
(in m/s)
Resultant direction:
(specify degrees and compass
headings)
Unit 1-4: One and Two-Dimensional Motion, Non-Trig Review I
©2010 by G. Meador – www.inquiryphysics.org
Inquiry Physics Unit 1-4 Test Review
Page 3
W rite the letter corresponding to the best answ er in the blank at the left of each question.
Assume air resistance is negligible.
7.
W hich of the following quantities is a vector which changes signs (directions) when an object that was
thrown upward stops rising and begins to fall?
A. velocity
B. speed
C. acceleration
D. time
8.
A ton of feathers and a ton of bricks are dropped from the same height on the moon. W hat happens?
A. The feathers strike the ground first.
B. The bricks strike the ground first.
C. The feathers and bricks strike the ground simultaneously.
D. Nothing hits the ground, because there is no gravity on the moon.
9.
W hen an object that was thrown upward reaches its highest point, which statement is true?
A. The acceleration switches from positive to negative.
B. The acceleration is zero.
C. The total displacement is zero.
D. The velocity is zero.
10.
A stone is thrown upward from atop a cliff and then lands at the base of the cliff. W hich statement
is true if the upward direction is considered "positive"?
A. The initial velocity of the stone is negative.
B. The acceleration of the stone is positive.
C. The final velocity of the stone is positive.
D. The final displacement of the stone is negative.
11.
Victor Velocity is standing on top of the roof of his house,
firing stones with his slingshot over a level field. He is
aiming straight outward, horizontally. If Victor pulls back
harder on the sling to shoot a stone, which of the following
quantities will be changed?
A. The vertical displacement of the stone.
B. The distance the stone travels.
C. The time it takes the stone to strike the ground.
D. The stone's initial vertical velocity.
12.
W hile riding at a constant speed on the train at the Kiddie Park,
Victor Vector playfully tossed Phluffy straight upward. During
the time Phluffy was in the air, the train moved forward one
meter. Phluffy landed...
A. in Victor’s loving arms.
B. one meter in front of Victor.
C. one meter behind Victor.
D. several meters behind Victor.
13.
An object is observed and a graph of its distance versus time is constructed. The graph has a slope
of +5.00 when the distance is measured in meters and the time is measured in seconds. The object
was...
A. moving at a constant speed of 5.00 m/s.
B. motionless.
C. decelerating.
D. accelerating at 5.00 m/s 2.
14.
Neglecting air resistance, when an object is thrown straight up, which of the following quantities is
NOT the same on the way down as on the way up?
A. acceleration
B. average speed
C. velocity
D. time of travel
Unit 1-4: One and Two-Dimensional Motion, Non-Trig Review I
©2010 by G. Meador – www.inquiryphysics.org
Inquiry Physics Unit 1-4 Test Review
15.
Page 4
Three forces simultaneously act on an object. The first is a 5 Newton force acting due east, the
second is a 3 Newton force acting due west, and the third is a 4 Newton force acting due east. W hat
is the resultant force?
A. 12 Newtons east
B. 6 Newtons east
C. 4 Newtons east
D. 2 Newtons west
A stone is tossed straight upward at +9.80 m/s.
16.
17.
18.
W hat is its velocity after 1.00 s?
A. +4.90 m/s
B. 0 m/s
C. -4.9 m/s
D. -9.80 m/s
W hat is its displacement after 1.00 s?
A. +4.90 m
B. 0 m
C. -4.90 m
D. -9.80 m
W hat is its acceleration at the top of its rise?
A. +4.90 m/s 2
B. 0 m/s 2
C. -4.90 m/s 2
D. -9.80 m/s 2
Questions 19 - 22 refer to the following situation:
A girl stood at first base on a level playing field and tossed a softball at an angle
of 35E above the horizontal. It was caught by another player over home base at
the same height above the ground as it was originally thrown.
19.
At which point along its trajectory was the softball travelling
the fastest?
A. Just after it was released.
B. W hen it reached its maximum height.
C. Just before it was caught.
D. Both A and C are correct if there is no air resistance.
20.
If the girl threw another softball with the same initial speed, but at 40E above the horizontal, . . .
A. it would have travelled a smaller horizontal distance.
B. it would have travelled a larger horizontal distance.
C. it would have travelled the same horizontal distance.
21.
W hat angle of release would make the softball travel as far as possible?
A. 15E
B. 30E
C. 45E
D.
65E
W hat was the softball's horizontal acceleration during its flight?
A. 0 m/s2
B. 2.45 m/s2
C. 4.90 m/s 2
D.
9.80 m/s 2
22.
23.
Draw the graphs for the free-fall motion of the projectile shown at right.
Unit 1-4: One and Two-Dimensional Motion, Non-Trig Review I
©2010 by G. Meador – www.inquiryphysics.org
INQUIRY PHYSICS TEST REVIEW II
Units 1-4: One and Two-dimensional Motion
Name
(Non-Trig)
In the space to the left, w rite the letter of the best answ er to each question. Assume air resistance is
negligible throughout. Answers to questions 1-8 are at the bottom.
1.
An object is observed and a graph of its distance versus time is constructed. The graph has a slope of +5.00 when
the distance is measured in meters and the time is measured in seconds. The object was...
a. moving at a constant speed of 5.00 m/s.
b. motionless.
c. decelerating.
d. accelerating at 5.00 m/s 2.
2.
Four force vectors act simultaneously on a body as shown below. W hat is the resultant force?
3.
The velocity (in m/s) vs. time (in s) graph of an object’s motion has a slope of +2. W hat does this indicate?
A. The object will travel 2 meters each second.
B. The object is accelerating at 2 m/s 2.
C. The object’s velocity is dropping by 2 m/s each second.
D. The object is rising at 2 m/s.
Questions 4 through 8 refer to the lettered sections of
the graph at right. An object’s displacement as it
moved backw ard and forw ard from its starting position
of zero is show n. (A section can be the answ er to more
than one question.)
4.
During which section did the object have the
largest constant speed?
5.
During which section was the object always
accelerating?
6.
During which section was the object always moving toward its starting position?
7.
During which section was the object moving forward at a constant speed?
8.
During which section was the object at rest?
Unit 1-4: One and Two-Dimensional Motion, Non-Trig Review II
©2010 by G. Meador – www.inquiryphysics.org
9.
A skier leaves the line at 3.00 m/sec downhill and accelerates uniformly at 1.25 m/s2 in the same direction. How fast
will the skier be moving after having gone 500 m?
35.5 m/s
10.
Firemen are practicing rescue operations in which people would have to jump from tall buildings into a net. For this
training exercise, a person hurls downward from a fire escape at 5.00 m/s and falls to a net 28.4 m below the fire
escape.
a. W hat will be the velocity of the person at the instant he or she hits the net?
24.1 m/s down
1.95 s
b.
How long will it take for the person to fall to the level of the net?
c.
How long after jumping would the person reach a velocity of 9.8 m/s downward?
0.490 s
11.
A bullet traveling 800.0 m/s horizontally hits a tree some distance away. If the bullet fell 0.100 m before it struck the
tree, how far away was that tree?
114 m
12.
A diver ran horizontally off the edge of a sheer cliff at 4.4 m/s. If the diver hit the water exactly 8.00 m from the base
of the cliff, how high was that cliff?
16.2 m
Unit 1-4: One and Two-Dimensional Motion, Non-Trig Review II
©2010 by G. Meador – www.inquiryphysics.org
PhysicsTest Review for Units 1 - 4
Nam e
One-Dim ensional Motion, Vectors, Falling Bodies, Projectiles
Trig Version
Test Objectives and Study Hints
M ultiple Choice
Covers all topics, but stresses projectile m otion concepts.
Be prepared to m ake or interpret graphs of objects in ANY of the m otions we have studied, including falling objects
and projectile m otion.
Be prepared for questions testing your understanding of the independence of horizontal and vertical m otion; review
concepts behind class dem os such as the sim ultaneous velocities apparatus, ballistic car, m onkey and hunter.
TO PREPARE:
Read all of your notes carefully.
Review the readings and worksheets on m otion graphs and projectile m otion.
Study the m ultiple choice questions on the “m easurem ent and m otion” and “vectors/falling bodies” quizzes. Be sure
you know the concept each questions deals with.
Do the accom panying concepts check and concept review questions.
Problems
Be prepared for problem s involving projectile m otion, falling bodies, and a com bination of both. For exam ple, som e
falling body problem s can becom e sim ple projectile m otion problem s testing your understanding of the independence
of horizontal and vertical m otion.
EXAMPLE: Review Problem #9
Be prepared for a m ultiple-step vector problem . For exam ple, you could be given two acceleration vectors along with
a tim e and asked to calculate the final velocity of an object that started from rest. You would add the accelerations
with vector m ath and then use v f=v i+at.
EXAMPLE: Review Problem #10
Be prepared for a m ultiple-step ground-based problem . For exam ple, som etim es the answer to one "part" of a
problem becom es a given in the second "part" — you m ay be given inform ation that will not directly lead to the answer,
but can be used to generate another given that leads to the answer. Or, you m ay need to split a problem into two parts
because the acceleration varies.
EXAMPLE: Review Problem #12
TO PREPARE:
Rework the problem s on the “m easurem ent and m otion” and “vectors/falling bodies” quizzes. Rework several different
types of projectile m otion problem - there are about five variants.
Up over level ground; dropped from height; shot angled downward from height; shot upward and land on cliff or land
in valley.
Do the accom panying review problem s.
Unit 1-4: One and Two-Dimensional Motion, Non-Trig Review II
Page 1 of 6
©2010 by G. Meador – www.inquiryphysics.org
Practice Problems
(answers are in italics at the right m argin; som e of these questions were written with 2 significant figures)
1.
Phyllis Physics set a course of 25.0E East of South in her airplane and a speed of 100 m/s. A storm during the flight
created a strong wind of 75.0 m/s aimed 65.0E N of E. W hat was the resultant velocity of her plane?
77.4 m/s at 17.0E S of E
2.
An angry Physics student wishes to drop an egg onto the head of poor Fred Freefall. He stations himself in a building
window 19.6 m above the level of Fred’s head. Determine how many seconds before Fred is directly beneath him that
he will have to drop the egg in order to get the desired splat.
2.00 s
3.
If a stone thrown from a bridge strikes the water 10.0 m below after 1.70 s, what was the stone's initial velocity?
2.45 m/s upward
4.
A shell leaves the muzzle of a howitzer at an angle of 45E above the horizontal and travels 7,500 m over level ground
before hitting an enemy bunker. W hat was the maximum height of the shell?
1900 m
5.
A skier leaves the line at 5.00 m/sec downhill and accelerates uniformly at 1.50 m/s2 in the same direction. How fast will
the skier be moving after having gone 500 m?
39.1 m/s
6.
Spaced-out Sue is speeding at a constant 3.500 × 104 km/h in her space coupe when she passes a galactic cop at rest by
the side of the Milky W ay. The instant Sue passes him, the cop accelerates after her at a constant rate. If it takes him
3.000 × 105 km to catch up with her, how much was he accelerating?
8,167 km/h 2
7.
A ball is thrown from the top of one building toward a tall building 50.0 meters away. The initial velocity of the ball
is 15.0 m/s at 40.0E above the horizontal. How far above or below its original level will the ball strike the opposite wall?
50.8 m below
8.
An object travelling at 5.0 m/s speeds up by 3.0 m/s each second over a time period of 8.0 seconds. W hat was the
object's average speed?
17 m/s
9.
A bullet is fired horizontally from a height of 78.4 m and hits the ground 1500 m away.
a) W ith what velocity does the bullet leave the gun?
375 m/s in the direction it was fired
b) At what angle did it strike the ground?
5.97E below the horizontal
10.
Phluffy can swim with a speed of 0.10 m/s in still water. One day Phluffy attempted to swim west across a part of a river
that was flowing from north to south with a speed of 0.35 m/s. W hat was Phluffy's displacement after swimming for
25 seconds?
9.1 m at 74E S of W
11.
A hose lying on the ground shoots a stream of water upward at an angle of 40E to the horizontal. The speed of the water
is 20 m/s as it leaves the hose. How high up will it strike a wall which is 8.0 m away?
5.4 m
12.
NASA uses a tall research tower in Cleveland, Ohio to study falling bodies and low-gravity conditions. Items are placed
in a “drag shield” so that they will not encounter air resistance - the shield is slowed by the air, but the items inside are
allowed to move downward freely within it. An airbag at the bottom of the tower can rapidly decelerate a package at
245 m/s2 over a distance of 0.964 m until it stops. Given this information, how far does a package drop before striking
the bag?
24.1 m
Unit 1-4: One and Two-Dimensional Motion, Non-Trig Review II
Page 2 of 6
©2010 by G. Meador – www.inquiryphysics.org
Concept Check (see reverse for answer analysis)
13. Two metal balls are the same size, but one weighs twice as much as the other. The balls are dropped
from the top of a two story building at the same instant of time. The time it takes the balls to reach the
ground below will be...
A. about half as long for the heavier ball.
B. about half as long for the lighter ball.
C. about the same time for both balls.
D. considerably less for the heavier ball, but not necessarily half as long.
E. considerably less for the lighter ball, but not necessarily half as long.
14. A NASA probe moving horizontally above the moon’s surface at
constant speed, to the right in the diagram, releases an instrument
package when it is directly above Point P. As seen from the lunar
surface, which path would the package most closely follow after
release?
15. The Roadrunner and Wile E. Coyote, who weighs twenty times more
than the bird, both run off a cliff edge over a level valley at the same
speed. If they remain in free fall with negligible air drag...
A. both hit the ground at approximately the same horizontal distance from the base of the cliff.
B. the bird travels twenty times the horizontal distance from the cliff base than does the coyote.
C. the coyote travels twenty times the horizontal distance from the cliff base than does the bird.
D. the bird travels quite a bit farther from the cliff base than the coyote, but not necessarily twenty times
as far.
E. the coyote travels quite a bit farther from the cliff base than the bird, but not necessarily twenty times
as far.
16. Three force vectors act simultaneously on
a body as shown at right. Which is the
resultant force?
17. A girl runs west at a constant speed of
3 m/s for one minute and then runs east
at the same speed for one minute. What
is the magnitude of her average velocity
over the entire two minutes?
A. 360 m/s
B. 180 m/s
C. 6 m/s
D. 3 m/s
E. 0 m/s
18. The motion of an object after it is released until it is
caught is graphed as shown at right. Which situation
corresponds to the graphs? (Assume air resistance
is negligible.)
A. An object thrown straight upward which is
caught below its starting point.
B. An object thrown straight downward which
bounces and is caught below its starting point.
C. An object thrown upward at some angle to the
horizon which is caught below its starting point.
D. An object thrown upward at some angle to the horizon which is caught above its starting point.
E. An object thrown downward at some angle to the horizon which bounces and is caught below its
starting point.
Unit 1-4: One and Two-Dimensional Motion, Non-Trig Review II
Page 3 of 6
©2013 by G. Meador – www.inquiryphysics.org
Concept Check Analysis:
13.
The correct answer is C. All objects fall with the same acceleration rate (same rate of velocity change) in the
absence of air resistance. Even with air resistance, objects of the same size and shape can be presumed to
encounter about the same drag.
Possible Misconceptions for Wrong Answers
A:
Mistaken belief that heavier objects fall faster than lighter ones.
B or E:
Possible mis-reading of question or answers.
D:
Mistaken belief that heavier objects fall faster than lighter ones, or misinterpretation of the effect of air resistance.
14.
The correct answer is D. A projectile will follow a parabolic path in the absence of air drag, and is immediately
acted upon by gravity upon release.
Possible Misconceptions for Wrong Answers
A or B:
Mistaken belief that mass makes things stop, or failure to realize that a projectile has same initial velocity as the projector.
C:
Failure to realize that the vertical velocity of a projectile in free-fall will change.
E or F:
Failure to realize that a projectile is affected by gravity immediately upon release, or mistaken belief that a projected object
receives some sort of forward “impetus” which later disappears.
15.
The correct answer is A. The horizontal velocity of a projectile is constant (its changing vertical motion will not
directly affect its horizontal motion) and all objects fall with the same acceleration rate in the absence of air
resistance.
Possible Misconceptions for Wrong Answers
B: Mistaken belief that heavier objects fall faster than lighter ones, or that lighter projectiles are not affected as quickly by gravity.
C
Mistaken belief that heavier projectiles retain their horizontal motion better than lighter ones. Possible mis-reading of question and
answers.
D: Mistaken belief that heavier objects fall faster than lighter ones, or that lighter projectiles are not affected as quickly by gravity. Also
possible that the effect of air resistance was misinterpreted.
E: Mistaken belief that heavier projectiles retain their horizontal motion better than lighter ones. Possible mis-reading of question and
answers, or that the effect of air resistance was misinterpreted.
16.
The correct answer is C. Draw the three vectors head-to-tail in any order and the
resultant is drawn from the tail of the first vector to the head of the last.
Possible Misconceptions for Wrong Answers
A: Resultant incorrectly drawn from finish to start rather than from start to finish, or student answered
with the equilibrant rather than the resultant.
B: Failure to correctly draw head-to-tail vector sum.
D: Mistaken belief that vectors cancel out; while the two diagonal vectors do cancel out, the vertical
vector remains.
17.
The correct answer is E. Velocity is the rate of change of vector displacement, not
scalar distance, and the girl’s overall displacement was zero since she returned to
her starting point. Alternatively, the velocity for the first minute was -3 m/s, if west is negative, but the velocity
for the second minute was then +3 m/s, and the average velocity calculation thus yields:
Possible Misconceptions for Wrong Answers
A or B: Confusing scalar distance with velocity; the distance in the first minute was 180 meters (3 m/s * 60 s = 180 m) so the total scalar
distance was 360 m.
C or D: Confusing speed with velocity; the average speed does not add up to 6 m/s, but it was 3 m/s since it ignores direction.
18.
The correct answer is D. The object is a projectile in free-fall because it has a steady horizontal velocity and
a changing vertical velocity. Its initial vertical velocity is positive, so it was projected upward. Its final vertical
velocity is negative, so it ended its motion while moving downward. Its final downward speed is smaller than
its initial upward speed, so it was caught before it had reached its original level (at which point it would have
regained its original speed).
Graphs Corresponding to the Wrong Answers
A.
B.
C.
E.
Unit 1-4: One and Two-Dimensional Motion, Non-Trig Review II
Page 4 of 6
©2013 by G. Meador – www.inquiryphysics.org
Additional Concept Review Questions (answers on reverse)
W rite the letter corresponding to the best answ er in the blank at the left of each question. Assume no air
resistance.
19. W hen an object that was thrown upward reaches its highest point, which statement is true?
A. The acceleration switches from positive to negative.
B. The acceleration is zero.
C.
The total displacement is zero.
D. The velocity is zero.
20. W hile riding at a constant speed on the train at the Kiddie Park, Victor Velocity
playfully tossed Phluffy straight upward. During the time Phluffy was in the air,
the train moved forward one meter. Phluffy landed...
A. in Victor’s loving arms.
B. one meter in front of Victor.
C.
one meter behind Victor.
D. several meters behind Victor.
21. An object is observed and a graph of its distance versus time is constructed. The graph has a slope of +5.00 when
the distance is measured in meters and the time is measured in seconds. The object was...
A. moving at a constant speed of 5.00 m/s.
B. motionless.
C. decelerating.
D. accelerating at 5.00 m/s 2.
22. Three forces simultaneously act on an object. The first is a 5 newton force acting due east, the second is a 3 newton
force acting due west, and the third is a 4 newton force acting due east. W hat is the resultant force?
A. 12 newtons east B. 6 newtons east
C. 4 newtons east
D. 2 newtons west
Questions 23 - 26 refer to the following situation:
A girl stood at first base on a level playing field and tossed a softball at an angle
of 35E above the horizontal. It was caught by another player over hom e base at
the sam e height above the ground as it was originally thrown.
23. At which point along its trajectory was the softball travelling the slowest?
A. Just after it was released.
B.
W hen it reached its maximum height.
C.
Just before it was caught.
D. Both A and C are correct if there is no air resistance.
24. If the girl threw another softball with the same initial speed, but at 55E above the horizontal, . . .
A. it would have risen to a lower height than before.
B.
it would have risen to the same height as before.
C.
it would have risen to a greater height than before.
25. W hat angle of release would make the softball travel as far as possible?
A. 15E
B. 30E
C. 45E
D. 65E
26. W hat was the softball's horizontal acceleration during its flight?
A. 0 m/s2
B. 2.45 m/s2
C. 4.90 m/s2
D. 9.80 m/s 2
Unit 1-4: One and Two-Dimensional Motion, Non-Trig Review II
Page 5 of 6
©2010 by G. Meador – www.inquiryphysics.org
Questions 27 through 31 refer to the lettered sections of the velocity vs. time graph, w hich is for an object
moving in straight-line horizontal motion.
(A section can be the answer to more than one
question, but each question has only one
answ er.)
27. During which section was the object
accelerating forward?
28. During which section did the object
actually m ove backward?
29. During which section was the object
at rest?
30. During which section was the
o b j e c t ’s a c c e le r a tio n a lw a ys
changing?
31. During which section was the object
m oving at a constant speed?
Questions 32 through 35 refer to the lettered sections of the displacement vs. time graph, w hich is also for
an object moving in straight-line horizontal motion.
(A section can be the answ er to more than one
question. Except as noted, each question has
only one answ er.)
32. During which section(s) was the
object at rest?
33. During which section was the object
always changing speed?
34. During which section did the object
m ove behind its starting point?
35. During which section was the object
m oving backward at a constant
speed?
Unit 1-4: One and Two-Dimensional Motion, Non-Trig Review II
Page 6 of 6
©2010 by G. Meador – www.inquiryphysics.org