Projectile Motion
Review Key
1. The acceleration due to gravity acts:
a. upward.
b. depending on the motion of the object.
c. downward.
d. toward outer space.

Fg
Since the net force is
downward, the resulting
acceleration is as well.
2. A bullet is fired at an angle of 45°. Neglecting air resistance, what is the direction of
acceleration during the flight of the bullet? Draw a force diagram of the bullet in
flight.
a. Downward.
Since the net force is

b. Dependent on the initial velocity.
Fg downward, the resulting
c. Upward.
acceleration is as well.
d. At a 45° angle.
3. A golfer drives her golf ball from the tee down the fairway in a high arcing shot.
When the ball is at the highest point of its flight
d. the horizontal velocity is non-zero and the vertical velocity is zero.
Since the only force acting on a projectile is the downward force of gravity, the
horizontal net force is zero and therefore the horizontal acceleration is zero. Hence,
the horizontal velocity is constant. At the highest point the ball is changing direction
and therefore its vertical velocity is instantaneously zero.
4. In the first practicum the ball was shot horizontally. What was the initial vertical

velocity (voy ) of the ball when it was shot?
d. 0 m
s
The initial velocity is
completely horizontal.
5. A soccer ball is kicked at a 55° angle with an initial velocity of 8 m . What is the
s
vertical velocity of the ball as it hits the ground?

a. 8 m
Since the completely
voy = vo sin 55
s
parabolic path is symmetric


b. − 8 m
m

vo
sin 55
voy = 8
s
voy
s


v y = −voy = −6.6 m

c. − 6.6 m
m
s
voy = 6.6

s
s
vx
(
)
6. Approximately how far will an object near Earth's surface fall in 3.0 s?
1
 

a. 44 m
 
y − y o = vo t + gt 2
y − yo = ?
b. 29 m
2
t = 3.0 s
 
c. 9.8 m
12
 
y − y o = −44 m
y
y
g
t
−
=

o
d. 88 m
vo = 0 m
2
s
1
 

2
y − y o = − 9.8 m 2 (3.0 s )
g = −9.8 m 2
s
s
2
(
)
Projectile Motion: Review Worksheet Key
page 2
7. For a projectile, what is the acceleration in the horizontal direction? Draw a force
diagram for the projectile anywhere in its path.
c. 0 m 2

s
Fg
Since there are no horizontal forces acting on a projectile
the horizontal net force and therefore the horizontal acceleration are zero.
8. A bullet is fired horizontally from a gun. At the same time a similar bullet is dropped
from the same height. In the absence of air resistance, the fired bullet will
b. hit at the same time as the dropped bullet.
The horizontal and vertical parts of projectile motion are independent of one another.
Since both bullets start with a vertical velocity of zero, have the same distance to fall
and have the same vertical acceleration − 9.8 m 2 , they will hit the ground at the
s
same time.
(
)
9. A 10 kg stone and a 100 kg stone are dropped from the roof of a building. Which will
hit the ground first? (Neglect air resistance)
a. They will hit at the same time.
Galileo’s Law of Falling Bodies says that in a vacuum all objects fall with the same
acceleration regardless of mass.
10. A ball thrown vertically upward reaches a maximum height of 30. m above the
surface of the Earth. At its maximum height, the speed of the ball is
a. 24 m
s
At the highest point the ball is changing direction and
m
b. 0
therefore its vertical velocity is instantaneously zero.
s
However, since gravity is an unbalanced force acting on
c. 3.1 m

s
the ball, the ball’s acceleration is still g = −9.8 m 2 .
s
d. 9.8 m
s
11. A red ball and a green ball are simultaneously thrown horizontally from the same
height. The red ball has an initial speed of 40. m and the green ball has an initial
s
m
speed of 20.
. Compared to the time it takes the red ball to reach the ground, the
s
time it takes the green ball to reach the ground will be
b. the same
The horizontal and vertical parts of projectile motion are independent of one another.
Since both bullets start with a vertical velocity of zero, have the same distance to fall
and have the same vertical acceleration − 9.8 m 2 , they will hit the ground at the
s
same time.
(
)
Projectile Motion: Review Worksheet Key
page 3
The rider and his bicycle in the diagram above are traveling to the right at a constant
speed. A ball is dropped from the hand of the cyclist.
12. Which set of graphs best represents the horizontal motion of the ball as it falls?
c.

x

vx
t
t
The horizontal motion of a projectile is constant velocity motion. Since the slope of a
graph of horizontal position vs. time is the horizontal velocity, the horizontal position
vs. time graph must be linear and the horizontal velocity vs. time graph must be
horizontal.
13. Which set of graphs best represents the vertical motion of the ball as it falls?
b.

y

vy
t
t
The vertical motion of a projectile is uniformly accelerated. Therefore as the ball
falls its vertical velocity increases in the negative direction. On a graph of vertical
position vs. time, the initial vertical position is positive as the ball is above the
ground, and the slope, which is the vertical velocity, must be increasing and
negative.
The slope of the vertical velocity vs. time graph is the vertical acceleration. As
gravity is the only force acting upon a projectile, the net force is constant and
downward and therefore the acceleration (slope) must also be constant and
negative.
Projectile Motion: Review Worksheet Key
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14. Which of the following statements are true of projectiles?
Answer: ABDEF
a. True - Free-falling objects, like projectiles, are objects upon which the only
significant force is gravity.
b. True - The only force on a projectile is gravity; air resistance must not be present
or must not have an influence upon the motion of the projectile.
c. False - Projectiles can be moving either upward or downward or at an angle to the
vertical. They must however be accelerating downward, consistent with
the force of gravity's effect on an object.
d. True - The force of gravity acts directly downwards upon an object, causing a
downward acceleration. Any projectile must be accelerating downwards
regardless of other features of its motion.
e. True - A projectile could be moving strictly in a vertical direction with no
horizontal motion. A ball thrown straight up in the air would be such a
case.
f. True - There is no rule about which direction a projectile must be moving at the
instant it is projected. It could begin its motion with an initial downward
velocity.
15. Which of the following statements are true of the horizontal motion of projectiles?
Answer: DFGHK
a. False - Many projectiles are moving from left to right and from right to left as they
simultaneously free fall. Such projectiles have a horizontal motion.
b. False - A projectile with a rightward motion (in addition to a vertical motion) will
have a constant velocity in the rightward direction. This is to say that it
has no horizontal acceleration as there is no horizontal net force.
c. False - A projectile has a constant horizontal velocity. However, the vertical
velocity will change by 9.8 m each second.
s
d. True - Absolutely true! Projectiles are objects being acted upon by gravity alone.
As such, there is a vertical acceleration but no horizontal acceleration.
The horizontal velocity of a projectile is either zero or a constant nonzero
value.
e. False - The vertical velocity of a projectile is 0 m at the peak of its trajectory; but
s
the horizontal component of the velocity at the peak is whatever the value
was when first launched since the horizontal velocity of a projectile is
constant.
f. True - For any two dimensional motion perpendicular components of the motion
are independent of each other. Any alteration in a vertical component will
not effect the horizontal components of motion.
g. True - The horizontal displacement can be calculated with the math model
 


x − xo = v x t , where v x is the horizontal velocity and t is the time. These
are the two variables which effect the horizontal displacement (range) of a
projectile.
Projectile Motion: Review Worksheet Key
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h. True - Since there is no horizontal acceleration for a projectile, the initial
horizontal velocity is equal to the final horizontal velocity.
i. False - The horizontal velocity is unchanging throughout the trajectory of a
projectile.
j. False - The range (or horizontal displacement) will increase as the angle is
increased from 0 degrees to 45 degrees. The maximum range occurs at
45 degrees. As the angle is further increased to values greater than
45 degrees, the horizontal displacement decreases.
k. True - As the launch speed is increased, the components of the initial velocity
(both the horizontal and the vertical) increase as well. This causes the
projectile to stay in the air for a longer period of time and to be moving
faster in the horizontal direction. The result is that increased launch
speeds always lead to increased horizontal displacements.
16. A football is kicked into the air at an angle of 45 degrees with the horizontal. At the
very top of the ball's path, its velocity is _______.
a. entirely vertical
b. entirely horizontal
c. both vertical and horizontal
d. not enough information given to know.
As a projectile rises towards its peak, its horizontal velocity remains constant while
its vertical velocity decreases. At its peak, its vertical velocity becomes 0 m . At
s
this instant in time, the velocity is entirely horizontal; there is no vertical component
to the velocity.
17. A football is kicked into the air at an angle of 45 degrees with the horizontal. At the
very top of the ball's path, its acceleration is _______. (Neglect the effects of air
resistance.)
a. entirely vertical
b. entirely horizontal
c. both vertical and horizontal
d. not enough information given to know.
As a projectile rises towards its peak, its horizontal velocity remains constant while
its vertical velocity increases. This is to say that the acceleration of the object is
completely vertical, not horizontal. At the peak and everywhere throughout the
trajectory, there is a vertical (downward) acceleration. In fact, a projectile is an
object upon which the only force is gravity. The unbalanced force of gravity causes
an acceleration which is in the same direction as the force - downward.
18. A football is kicked into the air at an angle of 45 degrees with the horizontal. At the
very top of the ball's path, the net force acting upon it is _______. (Neglect the
effects of air resistance.)
a. entirely vertical
b. entirely horizontal
c. both vertical and horizontal
d. not enough information given to know.
A projectile is an object upon which the only force is gravity. Since no other forces
act upon the object, the net force would be downward.
Projectile Motion: Review Worksheet Key
page 6
19. Which of the following statements are true of the vertical motion of projectiles?
Answer: CDFGHINPQ
a. False - The vertical component of a projectile's velocity is constantly changing. It
is the acceleration which has a value of 9.8 m 2 .
s
b. False - Projectiles are objects being acted upon by the unbalanced force of
gravity alone. As such, there is a vertical acceleration; the vertical velocity
is not constant, but rather is constantly changing.
c. True - See part b above.
d. True - A projectile has a vertical acceleration of 9.8 m 2 throughout the entire
s
trajectory since the force of gravity is constant throughout. This means
that the vertical velocity changes by the same amount, 9.8 m , during
s
each second of its motion.
e. False - All projectiles experience a downward acceleration, whether they are
moving upward or downward as the downward force of gravity is the only
force acting. Upward-moving projectiles have an upward velocity, but their
actual velocity values are getting smaller; that is, the projectile is slowing
down on the way to its peak.
f. True - This is a true statement. It could also be said that a projectile with an
upward component of motion also has a downward acceleration. All
projectiles accelerate in the downward direction. Period.
g. True - This is absolutely true since all projectiles on Earth accelerate at 9.8 m 2 .
s
h. True - At the peak of its trajectory, a projectile is in the process of changing
directions. The vertical velocity must change from a positive value (+ for
upward) to a negative value (- for downward).
i. True - For any two dimensional motion perpendicular components of the motion
are independent of each other. Any alteration in a vertical component will
not effect the horizontal components of motion.
j. False - A projectile launched at an angle forms a parabolic trajectory. However,
some projectiles are not launched from the same height at which they
land. The final height is not the same as the initial height and as such the
complete path is not symmetric. In such instances, the initial vertical
velocity is not equal to the final vertical velocity.
k. False - No! No! No! The vertical velocity is 0 m at the peak and the vertical
s
m
acceleration is − 9.8 2 throughout the entire trajectory since the force of
s
gravity is the only force acting on a projectile.
l. False - This would be a true description of the vertical velocity. But the vertical
acceleration is a constant value of − 9.8 m 2 throughout the entire
s
trajectory since the force of gravity is the only force acting on a projectile.
Projectile Motion: Review Worksheet Key
page 7
m. False - Not only is the magnitude of the vertical acceleration a constant value
throughout a projectile's trajectory, the direction is constant as well since
the downward force of gravity is the only force acting upon a projectile.
Projectiles at all times regardless of any other variable will accelerate
downwards at − 9.8 m 2 .
s
n. True - The initial vertical velocity has an effect on the time taken by a projectile to
rise towards its peak. As a result, any alteration in the vertical velocity will
alter the peak height of the projectile.
o. False - Upward-rising projectiles have a downward acceleration; this means they
are slowing down as they rise. The magnitude of their velocity is
decreasing. Downward moving projectiles also have a downward
acceleration; this means they are speeding up. The magnitude of their
velocity is increasing.
p. True - An increase in the angle of launch (from 0 to 90 degrees) will always

increase the vertical component of the initial velocity (voy ) . This increase
in the initial vertical velocity will lead to increased times for the projectile
rising towards its peak.
q. True - As the launch speed is increased, the components of the initial velocity
(both the horizontal and the vertical) increase as well. This causes the
projectile to stay in the air for a longer period of time and to be moving
faster in the vertical direction. The result is that increased launch speeds
always lead to increased heights for projectiles.

20. At what point in its path is the horizontal component of the velocity (v x ) of a
projectile the smallest?
a. The instant it is thrown.
b. Halfway to the top.
c. At the top.
d. As it nears the top.
e. It is the same throughout the path.
As a projectile rises towards its peak, its horizontal velocity remains constant while
its vertical velocity decreases. This is to say that the acceleration of the object is
vertical, not horizontal. Having a constant horizontal velocity, there is no point along
the trajectory where the horizontal velocity is smaller than at other points.

21. At what point in its path is the vertical component of the velocity (v y ) of a projectile
the smallest?
a. The instant it is thrown.
d. As it nears the top.
b. Halfway to the top.
c. At the top.
e. It is the same throughout the path.
As a projectile rises towards its peak, its horizontal velocity remains constant while
its vertical velocity decreases. During the upward portion of its trajectory, the vertical
velocity continuously decreases until it becomes 0 m at the peak. Thus, the vertical
s
velocity is as small as it will ever be when it is at the peak of the trajectory.
Projectile Motion: Review Worksheet Key
page 8
22. Which of the following statements are true of the time of flight for a projectile?
Answer: BCD
a. False - The time for a projectile to rise vertically to its peak (and subsequently fall
back to the ground) is dependent upon the initial vertical velocity.
Alteration in the horizontal velocity will only cause the projectile to have a
greater horizontal displacement (range).
b. True - Absolutely true. Projectiles with a greater vertical component of initial
velocity will be in the air for longer amount of times (assuming that the
direction of the initial vertical velocity is upward).
c. True - Since the vertical acceleration is constant, the projectile slows down on
the way up just as fast as it speeds up on the way down. Therefore, if it
starts and ends at the same height, the motion is completely symmetric.
If it takes 3 seconds to rise, it will take 3 seconds to fall.
d. True - For a constant launch angle, an increase in the initial velocity will increase
the initial vertical velocity. This results in an increased time for the
projectile to rise to its peak. So the projectile takes longer to get to the
peak, longer to fall from the peak and overall is in the air for a longer time.
e. False - Close, but very false. If it takes 3 seconds to rise to the peak, then it takes
3 seconds to fall from the peak. The 6 seconds is the total time of flight of
the projectile.
23. Roll a bowling ball off the edge of a table. As it falls, the horizontal component of its
velocity ___.
a. decreases
b. remains constant
c. increases
Once the ball leaves the table's edge, it becomes a projectile. As it falls, its
horizontal velocity remains constant while its vertical velocity decreases. This is to
say that the acceleration of the object is vertical, not horizontal. In fact, a projectile
is an object upon which the only force is gravity. This unbalanced force of gravity
causes an acceleration which is in the same direction as the force - downward.
24. A bullet is fired horizontally and hits the ground in 0.5 seconds. If it had been fired
with twice the speed in the same direction, it would have hit the ground in ____.
(Assume no air resistance.)
a. less than 0.5 s.
b. more than 0.5 s.
c. 0.5 s.
Once the bullet leaves the muzzle, it becomes a projectile (assuming no air
resistance). The motion of the bullet in the downward direction is independent of the
motion in the horizontal direction. That is to say, any alteration in a horizontal aspect
of its motion will not effect the motion in the vertical direction. Therefore, it would still
take 0.5 s to fall to the ground from this height regardless of the horizontal speed.
Projectile Motion: Review Worksheet Key
page 9
25. A projectile is launched at an angle of 15 degrees above the horizontal and lands
down range. For the same speed, what other projection angle would produce the
same downrange distance?
a. 30 degrees.
b. 45 degrees.
c. 50 degrees.
e. 90 degrees.
d. 75 degrees
For projectiles launched at angles, a launch angle of 45 degrees will provide the
largest horizontal displacement. Any two launch angles which are separated from
45 degrees by the same amount (for example, 40 degrees and 50 degrees, 30 degrees
and 60 degrees, and 15 degrees and 75 degrees) will provide the same horizontal
displacement.
26. Two projectiles are fired at equal speeds but different angles. One is fired at an
angle of 30 degrees and the other at an angle of 60 degrees. The projectile to hit the
ground first will be the one fired at (neglect air resistance) ____.
b. 60 degrees
c. both hit at the same time
a. 30 degrees
For projectiles launched at angles, a launch angle of 45 degrees will provide the
largest horizontal displacement. Launch angles greater than 45 degrees result in
larger vertical components of velocity; these stay in the air longer and rise to higher
heights. Launch angles less than 45 degrees result in smaller vertical components of
velocity; these do not rise as high and end up falling to the ground in shorter times.