2. Projectile motion
Projectile is a body thrown with an initial velocity
in the vertical plane and then it moves in two
dimensions under the action of gravity alone
without being propelled by any engine or fuel. Its
motion is called projectile motion.
The path of a projectile is called its trajectory.
1. A packet released from an airplane in
2. A golf ball in flight.
3. A bullet fired from a rifle.
4. A jet of water from a hole near the
bottom of a water tank.
4. If gravity were not present, a projectile would
travel in a constant straight line.
However, the presence of gravity forces
projectiles to travel in a parabolic trajectory,
thus gravity accelerates objects downwards.
The factors that affect the trajectory are:
a) Angle of projection
b) Projection velocity
c) Relative height of projection
6. Optimum Projectile Angle or Angle of
The angle at the projectile body is thrown
is called Optimum Projectile Angle or
Angle of projection
7. Optimum Projectile Angle or Angle of
If Relative Projection Height = 0, the optimum
angle = 450
If Relative Projection Height > 0 , the optimum
angle < 450
If Relative Projection Height < 0 , the optimum
angle > 450
8. The time of flight
The time of flight of a projectile motion is
the time from when the object is projected
to the time it reaches the surface. As we
discussed previously, T depends on the
initial velocity magnitude and the angle of
9. Maximum height
maximum height, which is the height of
the projectile when the vertical velocity is
zero and the projectile has only its
2 2 2 2
T & u usin
X u t at
X h &a g & t
10. Horizontal range
The range, R, which is the horizontal distance
that the projectile travels.
Range is the total horizontal
distance covered during the
time of flight.
From equation for horizontal
When t=T , x=R
R= uxT = ucos.2usinΦ/g
= u22sinΦcosΦ/g =
u2sin2Φ/g using 2sinΦcosΦ=
11. Equation of Trajectory (Path of projectile)
At any instant t
Also , y= u sinΦ.t - (1/2)gt2
Substituting for t
y= u.sinΦ.x/(u.cosΦ) - (1/2)g[x/(u.cosΦ)]2
y= x.tanΦ - [(1/2)g.sec2.x2 ]/u2
This equation is of the form y= ax + bx2 where 'a'
and 'b are constants. This is the equation of a
Thus, the path of a projectile is a parabola .
12. A lava rock is thrown horizontally at 15m/s from
the top of a cliff 44 m high.
a. How far form the base of the cliff does the
rock hit the ground?
xy = -44 m xx =?
ay= -9.8 m/s/s ax = 0
vi,y = 0 vi,x = 15m/s
vf,x = 0
13. First we need to solve for the time.
Use the formula xy = vit + 1/2at2
Time = 3 seconds
Now we know the time and we can find how far
from the base of the cliff it landed.
Use the formula v= x/t and
the distance is 45 m
14. The movie “The Gods Must Be
Crazy” begins with a pilot dropping
a bottle out of an airplane.
It is recovered by a surprised
native below, who thinks it is a
message from the gods.
If the plane was flying at an altitude
of 500 m, and the bottle lands 400
m horizontally from the initial
dropping point, how fast was the
15. An autographed baseball rolls off of a 0.70m
high desk and strikes the floor 0.25 m away
from the base of the desk. How fast was it
A. 0.77 m/s
B. 0.66 m/s
C. 0.54 m/s
16. Answer : A
A projectile is…
A. An object thrown or launched
into the air.
B. An object rolling down a hill
C. An object that is being hit by a
bat or other object
17. A cat chases a mouse across a 1.0 m
high table. The mouse steps out
of the way, and the cat slides
off the table and strikes the
floor 2.2m from the edge of the
table. What was the cat’s speed
when it slid off the table?
A. 5.9 m/s
B. 2.4 m/s
C. 4.9 m/s
18. A pelican flying along a horizontal
path drops a fish from a height of
5.4 m. The fish travels 8.0 m
horizontally before it hits the
water below. What is the
pelican’s initial speed?
A. 5.4 m/s
B. 7.7 m/s
C. 9.8 m/s
19. The path a projectile takes is
20. During a thunderstorm, a tornado lifts a cow to a
height of 125 above the ground. Increasing in
strength, the tornado flings the cow horizontally
with an initial speed of 90 m/s. How long does
the cow take to reach the ground? How far does
the cow travel before hitting the ground?
A. 5.05 s ; 454m
B 5.05 s ; 234 m
C. 4.03 s ; 454 m
D. 4.03 s ; 454 m
21. A ball is thrown horizontally
from the top of a building
from a height of 32.5 meters
above the ground. It lands 56
meters from the base of the
building. What is the initial
velocity of the ball? ( Two
22. Answer : C
In the x direction (ignoring air resistance),
the force acting on the projectile is________
A. The force that launched
C. There are no forces in the x direction
23. Answer : A
In the x direction (ignoring air resistance),
the acceleration of the projectile is____
B. 9.8 m/s
C. Increasing by 9.8 m/s every second.
24. Answer : c
In the x direction
resistance), the velocity
of a projectile______
C. Stays the
25. In the x direction, the object’s speed
______. (Ignoring air resistance)
C. Stays the same
26. Answer : A
A projectile is an object that the only forces
acting on it are air resistance and
28. Answer: B
If an object is shot horizontally, the initial
velocity in the y direction is_____________
A. 9.8 m/s
C. Dependent on the time
29. The organs fly off the edge of a table with a
velocity of ____m/s. The height of the table is 3
m and the horizontal range of the organs from
the base of the table is 15 m. How long does it
take for the organs to hit the ground?
B. 9.8 s
C. .78 s
D. .57 s
30. Answer : 145.5 m
A bridge is 180 m above a river. If a
goat is thrown from the bridge by a
troll with a horizontal velocity of 24
m/s. How far has the goat moved
horizontally when it hits the water?
31. A ball rolls off the edge of a table with a
horizontal velocity of ___ m/s. The height of
the table is 7 m and the horizontal range of the
ball from the base of the table is 15 m. What is
the initial speed of the ball.
A. 35 m/s
B. 24 m./s
C. 32 m/s
D. 13 m/s
32. Zeus throws a lightning bolt with a
horizontal velocity of 25 m/s. The
lightning bolt lands 30 meters away
from the cloud. How high is the
33. A ball is launched with an
initial velocity of 4.47
m/s at an angle of 66
degrees with the
a. What was the
maximum height the
b. How long did it take
the ball to return to the
c. What was its range?
34. A rugby player kicks a
ball from ground level
with an initial velocity
of 27.0 m/s at 30
degrees above the
What is the….
A. Hang time
C. Maximum height
35. A can is kicked with an initial speed of 60 m/s
at an angle of 30 degrees above the
horizontal. What s the can’s horizontal
displacement at the end of 4 seconds?
36. Answer : C
A baseball is hit with a vertical speed of 20
m/s and a horizontal speed of 30 m/s. How
long will the ball remain in the air?
A. 2 seconds
B. 3 seconds
C. 4 seconds
D. there is no way to tell
37. A girl kicks a robot and the head flies off at
an angle of 20 degrees. The head would
have landed at the same spot if it had been
kicked at an angle of:
A: 40 degrees
b. 70 degrees
C. 45 Degrees
D. 25 degrees
38. The horizontal and
of the initial velocity
of a football are 24
m/s and 7 m/s
is the initial velocity
of the football?
39. A bride throws a
bouquet with an
initial velocity of 27
m/s at an angle of 25
degrees above the
horizontal. How high
above the projection
point is the bouquet
after 1.8 s?
40. Answer : C
A ball is thrown at an angle of 45
degrees above the horizontal
with an initial velocity of
20m/s. What is the total time
of flight of the ball before it
hits the ground?
A. 9.8 s
B. 6.1 s
C. 2.9 s
D. 4.9 s
41. Answer : D
A man kicks a soccer ball with an initial
velocity of 25 m/s at an angle of 30°above
the horizontal. The horizontal component of
the velocity of the ball is described by one
of the following statements.
A) It changes uniformly.
B) It is zero.
C) It is 25 m/s.
D) It remains constant during the ball's
42. Answer : C
A man is launched from a cannon
with an initial velocity of 26 m/s at
an angle of 20 degrees above the
horizontal. How high above the
projection point is the man after 1.4
A. 8.2 m
B. 24 m
C. 2.8 m
43. Suppose that an angel flying
60 m/s, at a height of 300m,
dropped a sack of halos.
How far from the point of
release would the sack have
traveled when it struck the
44. A snowball is thrown at some
angle above the horizontal with a
certain velocity. It reaches its
highest point and starts falling
down. What is the velocity of the
snowball at the highest point of
A. 9.8 m/s
B. It is equal to its initial
D. It is equal to its initial vertical
Answer : B
45. Answer : A
Which of the following conditions is met when a
projectile reaches its maximum height?
A. Vertical component of the velocity is zero.
B. Vertical component of the velocity is maximum.
C. Horizontal component of the velocity is
D. Acceleration in the vertical direction is zero.
46. Answer : C
What is the range of a projectile?
A. The total trajectory that the projectile travels.
B. The vertical distance that the projectile travels.
C. The horizontal distance that the object travels.
D. Twice the maximum height of the projectile.
47. Answer : B
The horizontal and vertical
components of the initial
velocity of a soccer ball are
24m/s and 7 m/s
respectively. What is the
initial velocity of the soccer
A) 31 m/s
B) 25 m/s
C) 17 m/s
D) 42 m/s
48. Define the flight time or hang time of a trajectory.
A. Time taken by the projectile to reach the
B. The maximum height reached by the projectile
divided by the magnitude of the vertical velocity.
C. The total time the projectile was in the air.
D. Half the total time the projectile was in the air.
49. Answer : B
. What is the maximum
height obtained by a
125g rock that is slung
from a slingshot at an
angle of 78° from the
horizontal with an
initial velocity of 18
A. 0.70 m
B. 16 m
C. 32 m
D. 33 m
50. An orange is dropped at the same time a bullet is
shot from a gun ( ignoring air resistance). Which
of the following is true?
A. The acceleration due to gravity is greater for the
orange because the orange is heavier.
B. Gravity acts less on the bullet than on the orange
because the bullet is moving so fast.
C. The velocities will be the same.
D. The two objects will hit the ground at the same
51. A baseball player throws a ball from left field
toward the home plate. ( Neglecting air resistance)
At the instance the ball reaches its highest point,
what is the direction of the ball’s velocity?
D. There is not enough information to say
52. If an object is shot upward at an angle (no air) and
lands at the same height it is shot, the final velocity
B. The same as the initial velocity
C. Negative the initial velocity