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HW - FREE FALL - HONORS
1. A ball is thrown upwards with a speed of 24 m/s. Take the acceleration due to gravity to be 10 m/s2.
(a) When is the velocity of the ball 12.0 m/s ?
(c) What is the displacement of the ball at those times?
(e) What is the maximum height reached by the ball?
(b) When is the velocity of the ball - 12.0 m/s?
(d) What is the velocity of the ball 1.50 s after launch?
2. A stone is thrown vertically upwards with an initial speed of 10.0 m/s2 from a cliff that is 50.0 m high.
(a) When does it reach the bottom of the cliff?
(b) What speed does it have just before hitting the ground?
(c) What is the total distance traveled by the stone?
Take the acceleration due to gravity to be 10 m/s2.
3. A rock is thrown vertically down from the roof of 25.0 m high building with a speed of 5.0 m/s.
(a) When does the rock hit the ground?
(b) With what speed does it hit the ground?
Take the acceleration due to gravity to be 10 m/s2.
4. A window is 1.50 m high. A stone falling from above passes the top of the window with a speed of 3.00 m/s. When will it pass
the bottom of the window? (Take the acceleration due to gravity to be 10 m/s2.)
5. A ball is dropped from rest from a height of 20.0 m. One second later a second ball is thrown vertically downwards. If two balls
arive at the ground at the same time, what must have been initial velocity of the second ball? (Take the acceleration due to
gravity to be 10 m/s2.)
6. * A ball is dropped from rest from the top of a 40.0 m building. A second ball is thrown downward 1.0 s later.
(a) If they hit the ground at the same time, find the speed with which the second ball was thown.
(b) What is the ratio of the speed of the thrown ball to the speed of the other as they hit the ground?
(Take the acceleration due to gravity to be 10 m/s2.)
7. * Two balls are dropped from rest from the same height. One of the balls is dropped 1.00 s after the other. What distance
separates the two balls 2.00 s after the second ball is dropped?
(Take the acceleration due to gravity to be 10 m/s2.)
8.
* A mass is thrown upwards with an initial velocity of 30 m/s. A second mass is dropped from directly above, a height of 60 m
from the first mass, 0.5 s later. When do the masses meet and how high is the point where they meet?
9. * A hot air balloon is rising vertically at constant speed 5.0 m/s. A sandbag is released and it hits the ground 12.0 s later.
(a) With what speed does the sandbag hit the ground?
(b) How high was the balloon when the sandbag was released?
(c) What is relative velocity of the sandbag with respect to the balloon 6.0 s after it was dropped?
Assume that the balloon's velocity increased to 5.5 m/s after releasing sandbag.
Take the acceleration due to gravity to be 10 m/s2.
10. An object with initial velocity 20 m/s and initial displacement - 75 m experiences an acceleration of - 2 m/s2 . Draw the
displacement - time graph for this motion for the first 20 s.
11. An object moves in a straight line with an acceleration that varies with time as shown:
Initially the velocity of the object is 2.00 m/s.
(a) Find the maximum velocity reached in the first 6.00 s of this motion.
(b) Draw a graph of the velocity versus time.
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12. A stone is thrown vertically up from the edge of a cliff 35.0 m from the ground. The initial velocity of the stone is 8.00 m/s
(a) How high will the stone get?
(b) When will it hit the ground?
(c) What velocity will it have just before hitting the ground?
(d) What distance will the stone have covered?
(e) What is the average speed and average velocity fro this motion?
(f) Make a graph to show the variation of displacement with time.
(g) Make a graph to show the variation of velocity with time.
Take the acceleration due to gravity to be 10 m/s2.
13. A ball is thrown upward from the edge of a cliff with velocity 20.0 m/s. It reaches the bottom of the cliff 6.0 s later.
(a) How hight is the cliff?
(b) With what speed does the ball hit the ground?
14. A rocket accelerates vertically upwards from rest with a constant acceleration of 4.00 m/s2 . The fuel lasts for 5.00 s.
(a) What is the maximum height achieved by this rocket?
(b) When does the rocket reach the ground again?
(c) Sketch a graph to show the variation of the velocity of the rocket with time from the time of launch to the time it falls to the
ground. Take the acceleration due to gravity to be 10 m/s2.
15. The baseball catcher throws a ball vertically upward and catches it in the same spot as it returns to the mitt. At what point in
the ball’s path does it experience zero velocity and nonzero acceleration at the same time?
a. midway on the way up
b. at the top of its trajectory
c. the instant it leaves the catcher’s hand
d. the instant before it arrives in the catcher’s mitt
16. Ball A is dropped from rest from a window. At the same instant, ball B is thrown downward; and ball C is thrown upward from
the same window. Which statement concerning the balls is necessarily true if air resistance is neglected?
a. At some instant after it is thrown, the acceleration of ball C is zero.
b. All three balls strike the ground at the same time.
c. All three balls have the same velocity at any instant.
d. All three balls have the same acceleration at any instant.
e. All three balls reach the ground with the same velocity.
17. A rock is thrown vertically upward from the surface of the earth. The rock rises to some maximum height and falls back
toward the surface of the earth. Which one of the following statements concerning this situation is true if air resistance is
neglected?
a. As the ball rises, its acceleration vector points upward.
b. The ball is a freely falling body for the duration of its flight.
c. The acceleration of the ball is zero when the ball is at its highest point.
d. The speed of the ball is negative while the ball falls back toward the earth.
e. The velocity and acceleration of the ball always point in the same direction.
18. A ball is in free fall. Its acceleration is:
a.
b.
c.
d.
e.
downward during both ascent and descent
downward during ascent and upward during descent
upward during ascent and downward during descent
upward during both ascent and descent
downward at all times except at the very top, when it is zero
19. A ball is in free fall. Upward is taken to be the positive direction. The displacement of the ball is:
a.
b.
c.
d.
e.
positive during both ascent and descent
negative during both ascent and descent
negative during ascent and positive during descent
positive during ascent and negative during descent
none of the above
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20. A baseball is thrown vertically into the air. The acceleration of the ball at its highest point is:
a.
b.
c.
d.
e.
9.8 m/s2 down
9.8 m/s2 up
changing suddenly from 9.8 m/s2 up to 9.8 m/s2 down
zero
cannot be calculated without knowing the initial velocity
21. Which one of the following statements is correct for an object released from rest?
a.
b.
c.
d.
e.
The average velocity during the first second of time is 4.9 m/s
During each second the object falls 9.8 m
The acceleration changes by 9.8 m/s every second
The object falls 9.8 m during the first second of time
The acceleration of the object is proportional to its weight
22. An object is shot vertically upward. While it is rising:
a.
b.
c.
d.
e.
its velocity and acceleration are both upward
its velocity is upward and its acceleration is downward
its velocity and acceleration are both downward
its velocity is downward and its acceleration is upward
its velocity and acceleration are both decreasing
23. The Steamboat Geyser in Yellowstone National Park, Wyoming is capable of shooting its hot water up from the ground with a
speed of 48.0 mIs. How high can this geyser shoot?
24. A baby blue jay sits in a tall tree awaiting the arrival of its dinner. As the mother lands on the nest, she
drops a worm toward the hungry chick’s mouth, but the worm misses and falls from the nest to the
ground in 1.50 s. How high up is the nest?
25. At Six Flags Great Adventure Amusement Park in New Jersey, a popular ride known as “Free Fall” carries passengers up to a
height of 33.5 m and drops them to the ground inside a small cage. How fast are the passengers going at the bottom of this
exhilarating journey?
26. A unique type of basketball is played on the planet Zarth. During the game, a player flies above the basket and
drops the ball in from a height of 10 m. If the ball takes 5.0 s to fall, find the acceleration due to gravity on
Zarth.
27. Pepe, the clown, is jumping on a trampoline as Babette, the tightrope walker, above him suddenly loses her balance and falls
off the tightrope straight toward Pepe. Pepe has just started upward at 15 m/s when Babette begins to fall. Pepe catches her in
midair after 1.0 s. a) How far has Babette fallen when she is caught by Pepe? b) What is Babette’s velocity at the time of
contact? c) What is Pepe’s velocity at the time of contact? d) How far above the trampoline was Babette before she fell?
28. Mr. DeFronzo has just learned that he won the Presidential Award for Excellence in Science Teaching. He runs to the open
window and throws his red marking pen into the air with an initial upward speed of 5.00 m/s. a) If the window is 12.0 m above
the ground, what is the velocity of the pen 1.0 s after it is thrown? b) How far has the pen fallen from its starting position after
2.0 s? c) How long does it take the pen to hit the ground?
HW - FREE FALL
1. (a) 1.2 s
2. (a) 4.32 s
3. (a) 1. 79 s
Answer Section
(b)
3.6 s
(b)
(b)
33.2 m/s
22.9 m/s
(c)
21.6 m
(c)
60 m
(d)
9.0 m
(e)
28.8 m
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4. 0.324 s
5. 15 m/s, downwards
6. (a) 12.7 m/s
(b) 1.1
7. 25 m
8.
g = -10 m/s2
first ball :
y1 = 30 t - 5 t2
second ball:
y2 = 60 - 5(t - 0.5)2
Displacements are the same when the balls meet:
30 t - 5 t2 = 60 - 5(t - 0.5)2
t = 2.35 s
9. (a) 115 m/s
(b) 660 m
(c) - 60.5 m/s
10. The displacement is given by x = xinitial + vinitial t + (a/2) t2
a = g = - 10 m/s2
x = - 75 + 20 t - 5 t2
11. (a) v = vinitial + a1 t1 + a2 t2 = 2.00 + (3)(2) + (6)(2) = 20 m/s
(b)
12. (a) 3.2 m from top of cliff
(b) 3.56 s
(d) 41.4 m
average velocity = - 9.83 m/s
(c) - 27.6 m/s
(e) average speed = 11.6 m/s
13.
14.
15.
20.
23.
(a)
60 m
(b) 40 m/s
(a) 70 m
B
A
(b) 10.7 s from the start
16. D
21. A
17. B
22. B
18. A
19. D
vf = 0 m/s
g= 10.0m/s2
y =( vf2 - vi2)/2g = —115 m
vi = 48.0 m/s
vf2 = vi2 + 2 gy
24. vi = 0 m/s
g = 10.0 m/s2
y = 11.3 m
y = vit + ½ g t2
t = 1.50 s
25. vf2 = vi2 + 2 gd = 670. m2/s2
27. a) y = vit + ½ g t2
= 5.0 m
b) vf = vi +
gt
c) vf = v0 +
gt
d) y = vit + ½ g t2
+
26.
vf = 25.9 m/s
g = 0.8 m/s2
= 10 m/s downwards
= -15 m/s + (10.0)(1.0) = - 5.0 m/s
or
= (-15)(1.0) + (1/2)(10.0)(1.0)2 = - 10.0 m
So 5.0 m + 10 m = 15 m
28. g = 10.0 m/s2
a) vf = vi + gt
= 5 m/s down
b) y = vit + ½ g t2
= 10.0 m
down
c) vf2 = vi2 + 2 gy = 265 m2/s2
vf = 16.3 m/s down
vf = v 0 +
gt
t = 2.13 s
5.0 m/s upward
or
10.0 m upward