Concepts of Physics
Mr. Kuffer
A stone is thrown horizontally at a speed of +5.0 m/s from the top of a
cliff 78.4 m high.
 How long does it take the stone to reach the bottom of the
cliff?
 How far from the base of the cliff does the stone strike the
ground?
 What are the horizontal and vertical components of the
velocity of the stone just before it hits the ground?
1
Projectile Motion
Can you get the Ball in the Cup?
Mr. Kuffer
Objective:
The purpose of this lab is to demonstrate an understanding of the
independence of vertical and horizontal velocities of a projectile by solving a
problem of a projectile launched horizontally in a lab setting.
Materials:
Ball-bearing, race-car track, stopwatch, meter stick
Styrofoam cup, lab table, calculator, class notes, text
Setup / Procedure:
To be explained in class. If absent, be prepared to gather notes from
a lab partner. Remember to draw any diagram(s) when needed.
Horizontal launch (to take place in the classroom) – Using vx and
dy (height) of the Ball bearing, find its dx (range), vyf, and t.
Theory:
The independence of vertical and horizontal motion and our motion
equations (Use Textbook) can be used to determine the position of thrown
objects. If we call the horizontal displacement dx and the initial horizontal
velocity vx then, at time t, (Note: vxf = vxi)
dx = vxt
The equations for an object falling with constant acceleration, g,
describe the vertical motion. If dy is the vertical displacement, the initial
vertical velocity of the object is vy. At time t, the vertical displacement is
dy = vyi t + ½ gt2
Using these equations, we can analyze the motion of projectiles. (Be
sure to retain the independence of the vertical and horizontal components)
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Analysis Questions:
1. The Ball bearing rolls “without friction” across the table at a
CONSTANT VELOCITY. When it reaches the end of the table, it flies
off and lands on the ground.
a) Draw the situation above, drawing vectors showing the
Acceleration of the Ball-bearing at two positions while it is
on the table and at three more when it is in the air. Draw all
vectors to scale.
2. For the Ball bearing in question 1,
a) Draw vectors showing the horizontal and vertical
components of the Ball bearing’s velocity at the five points.
b) Using a different color, draw the total velocity vector at the
five points.
3. Determine the time the ball will be in flight.
4. Determine where the ball will land.
5. What will the final velocity be in the …
a) X direction?
b) Y direction?
6. What will the total final velocity equal?
3
4
Name:__________
Projectile Motion
Period:_____
1. You accidentally throw your car keys horizontally at 6.0 m/s from a cliff
(oops!) 64 m high. How far away from the base of the cliff should you
look for your keys?
X
Y
2. An airplane traveling 1001 m above the ocean at 135 km/h is to drop a box
of supplies to shipwrecked victims below.
a) How many seconds before being directly overhead should the box
be dropped?
X
Y
b) What is the horizontal distance between the plane and the victims
when the box is dropped?
3. A projectile is an object that has independent x and y components that
moves through the air only under the influence of _________.
a) others
b) x components
c) y components
d) gravity
4. The horizontal and vertical components of a projectile are
_____________.
a) the same
b) dependent
c) independent
d) simultaneous
6.
The path of a projectile is called a ___________.
a) launch angle
b) intercept
c) trajectory
d) range
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Study Guide:
Additional Horizontal Projectile Practice Problems
9. A stone is thrown horizontally at a speed of 5.0 m/s from the top of a
cliff 78.4 m high.
B) 20 m
a. How long does it take the stone to reach the bottom of the cliff?
b. How far from the base of the cliff does the stone hit the ground?
C) Vx = 5.0 m/s
Vy = 39 m/s
c. What are the horizontal and vertical components of the
stones velocity just before it hits the ground?
A) 4.0 s
10. How would the three answers to problem 9 change if…
a. The stone were thrown with twice the horizontal speed?
b. The stone were thrown with the same speed, but the cliff
were twice as high?
10 A) a) 4.0 s
b) 40 m
c) Vx = 10 m/s
Vy = 39 m/s
10 B) a) 5.7 s
b) 28 m
c) Vx = 5.0 m/s
Vy = 55 m/s
11. A steel ball rolls with constant velocity across a tabletop
0.950 m high. It rolls off and hits the ground 0.352 m from the edge
V = 0.8 m/s
of the table. How fast was the ball rolling?
6
Angular Projectile Motion
Daniel Sepulveda punts a football
at 45˚ with an initial velocity of 24
m/s.
1. What is the hang time of the
ball?
2. What does the punt ‘net’,
assuming the return man
signals for a fair catch?
3. What was the maximum
height of the punt?
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Name:__________
Date:_________
Period:_____
Angular Projectile Motion
5. An arrow is shot 30˚ above the horizontal. Its velocity is 49 m/s and it
hits the target.
X
a) What is the maximum height the arrow will attain?
Y
b) The target is at the height from which the arrow was shot. How
far away is it?
6. A soccer player kicks a ball into the air at an angle of 31˚ above the
horizontal and it lands at the same height from which it was kicked. The
initial velocity of the ball is 35 m/s.
X
7. How long is the soccer ball in the air?
Y
8. What is the maximum horizontal distance traveled by the
soccer ball?
9. What I the maximum height reached by the soccer ball?
8
10. Romeo is chucking pebbles gently up to Juliet’s window. He is standing at
the edge of a rose garden 8.0 m below her window and 9.0 m from the
base of the wall. If he wants the pebbles to hit the window with only a
horizontal component of velocity, how fast will the pebbles be going
when they hit her window?
X
Extra Practice
Y
Solution
12) t = 2.76 s
dx = 64.6 m
dy = 9.27 m
13) t = 4.78 s
dx = 64.5 m
dy = 27.9 m
9
Ball Toss
When a juggler tosses a ball straight upward, the ball slows down until it reaches the top
of its path. The ball then speeds up on its way back down. A graph of its velocity vs. time
would show these changes. Is there a mathematical pattern to the changes in velocity?
What is the accompanying pattern to the position vs. time graph? What would the
acceleration vs. time graph look like?
In this experiment, you will use a Motion Detector to collect position, velocity, and
acceleration data for a ball thrown straight upward. Analysis of the graphs of this motion
will answer the questions asked above.
OBJECTIVES

Collect position, velocity, and acceleration data as a ball travels straight up and
down.
 Analyze the position vs. time, velocity vs. time, and acceleration vs. time graphs.
 Determine the best fit equations for the position vs. time and velocity vs. time
graphs.
 Determine the mean acceleration from the acceleration vs. time graph.
MATERIALS
computer
Vernier computer interface
Logger Pro
Vernier Motion Detector
ball
PRELIMINARY QUESTIONS
1. Think about the changes in motion a ball will undergo as it travels straight up and
down. Make a sketch of your prediction for the position vs. time graph. Describe in
words what this graph means.
2. Make a sketch of your prediction for the velocity vs. time graph. Describe in words
what this graph means.
3. Make a sketch of your prediction for the acceleration vs. time graph. Describe in
words what this graph means.
PROCEDURE
1. Connect the Vernier Motion Detector to the DIG/SONIC 1 channel of the interface.
2. Place the Motion Detector on the table. Cover the Motion Detector with the protective
cage.
3. Open the file “06 Ball Toss” from the Physics with Computers folder.
4. In this step, you will toss the ball straight upward above the Motion Detector and let it
fall back toward the Motion Detector. This step may require some practice. Hold the
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ball directly above and about 0.5 m from the Motion Detector. Click
to begin
data collection. You will notice a clicking sound from the Motion Detector. Wait one
second, then toss the ball straight upward. Be sure to move your hands out of the way
after you release it. A toss of 0.5 above the Motion Detector works well. You will get
best results if you catch and hold the ball when it is about 0.5 m above the Motion
Detector.
5. Examine the position vs. time graph. Repeat Step 4 if your position vs. time graph
does not show an area of smoothly changing position. Check with your teacher if you
are not sure whether you need to repeat the data collection.
ANALYSIS
1. Sketch the three motion graphs in your lab notebook. The graphs you have recorded
are fairly complex and it is important to identify different regions of each graph.
Click the Examine button, , and move the mouse across any graph to answer the
following questions. Record your answers directly on the sketched graphs.
a) Identify the region when the ball was being tossed but still in your hands:

Examine the velocity vs. time graph and identify this region. Label this on the
graph.
 Examine the acceleration vs. time graph and identify the same region. Label the
graph.
b) Identify the region where the ball is in free fall:

Label the region on each graph where the ball was in free fall and moving upward.
 Label the region on each graph where the ball was in free fall and moving
downward.
c) Determine the position, velocity, and acceleration at specific points.

On the velocity vs. time graph, decide where the ball had its maximum velocity, just
as the ball was released. Mark the spot and record the value on the graph.
 On the position vs. time graph, locate the maximum height of the ball during free
fall. Mark the spot and record the value on the graph.
 What was the velocity of the ball at the top of its motion?
 What was the acceleration of the ball at the top of its motion?
2. The motion of an object in free fall is modeled by y = v0yt + ½ gt2 (equation 6), where
y is the vertical position, v0y is the initial2 velocity in the y direction, t is time, and g is
the acceleration due to gravity (9.8 m/s ). This is a quadratic equation whose graph
is a parabola. Your graph of position vs. time should be parabolic. To fit a quadratic
equation to your data, click and drag the mouse across the portion of the position vs.
time graph that is parabolic, highlighting the free-fall portion. Click the Curve Fit
button, , select Quadratic fit from the list of models and click
. Examine the
fit of the curve to your data2and click
to return to the main graph. How closely
does the coefficient of the t term in the curve fit compare to ½ g? ( 1/2 g is 4.9…
what is ‘coefficient’? How well do they compare?)
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3. The graph of velocity vs. time should be linear. To fit a line to this data, click and
drag the mouse across the free-fall region of the motion. Click the Linear Fit button,
. How closely does the coefficient of the t term in the fit compare to the accepted
value for g?
4. The graph of acceleration vs. time should appear to be more or less constant. Click
and drag the mouse across the free-fall section of the motion and click the Statistics
button, . How closely does the mean acceleration value compare to the values of g
found in Steps 2 and 3?
5. List some reasons why your values for the ball’s acceleration may be different from
the accepted value for g.
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Angular
Projectile Lab
1. Label the max dy and dx.
2. Draw velocity vectors for each point of the projectile’s
trajectory.
3. What is the max height of the projectile if it is launched
with an initial velocity of 4.3 m/s?
4. How long is the ball in the air?
5. What is the range of the projectile if the cart is traveling
at 1.2 m/s?
HINT:
“WHAT GOES UP… MUST
____________________________... BEFORE IT COMES
BACK DOWN IT HAS GOT TO _____________”
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Projectiles Launched at an Angle
Physics
Projectile Launcher Lab
North Allegheny SH
Mr. Kuffer
Launcher
#
Names:
Period:
Determining the Range and Apex of a Projectile
Background
From class, you know that a projectile is something that is thrown or fired but not self propelled.
You also know that because of gravity pulling the projectile from its straight line path, it will
ideally follow a parabolic path. Also, you know that this seemingly complicated motion can be
simplified by looking at the two dimensions separately. Purpose
The purpose of this lab is to determine the range of a projectile launcher and the height at apex.
As a test, we will fire a plastic marble projectile through a hoop at the apex and into a container at
the maximum range.
Procedure
Step 1-Determining the initial velocity of the launcher
Using the supplied bracket, attach a photogate to the end of the projectile launcher, as shown
below.
photogate
launcher
bracket
Using gate mode, measure the time the ball will break the photogate’s beam. Prior to
loading the launcher, push the ramrod into the launcher, cocking the launcher to MEDIUM
RANGE. Shoot the launcher in a safe direction, and do not catch the ball. Record the broken
beam time below. The diameter of the ball is exactly 1 inch or .0254 m. Determine the
initial velocity of the launcher on medium range by dividing.
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distance =
0.0254 m
=
velocity=
m/sec
time =
Step 2 - Determining range of the launcher
Clamp the launcher on the end of the table. Set the launcher’s angle so that when marble is
launched on SHORT range, that it lands somewhere on the two adjacent tables.
Marble lands
somewhere on
two tables
Determine where your container should be placed to catch the marble AT THE SAME
HEIGHT IT WAS LAUNCHED by resolving your initial velocity into x- and y-components,
and then working out your horizontal and vertical mathematics.
m/sec
m/sec
m/sec
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(X)
(Y)
acceleration = 0
acceleration = g
Try your experiment. Did it work on the first try? What are some possible sources of
error?
Continue trying and revising until you can reliably get the marble into your container.
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Step 3-Determining apex of the launcher
Obtain one of the apex hoops. Place it on a ring stand as shown below.
Calculate mathematically how high the apex ring should be so that the marble can pass
through the ring on route to the container. Show your work below.
Try your experiment. Did it work on the first try? What are some possible sources of
error?
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