Projectile Motion WS

1. The diagram below shows the path of a projectile in the absence of air resistance.
Vertical
position

Horizontal position

Which one of the following diagrams best represents the path of the projectile under the same initial
conditions when the air resistance is taken into account? (The path in absence of air resistance is shown for
comparison as a dotted line.)

A. Vertical B. Vertical
position position

Horizontal position Horizontal position

C. Vertical D. Vertical
position position

Horizontal position Horizontal position

(1)

2. A stone is thrown from O at an angle to the horizontal. Which sketch below best shows the path of the
stone when air resistance is not neglected? On each sketch, the broken line shows the path for the same
stone in a vacuum.

A. B.

O O

C. D.

O O
(1)

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3. Which one of the following is a true statement concerning the vertical component of the velocity and the
acceleration of a projectile when it is at its maximum height? (The acceleration of free fall is g.)

Vertical component of velocity Acceleration

A. maximum zero
B. maximum g
C. zero zero
D. zero g
(1)

4. A ball is thrown horizontally from the top of a cliff. Air resistance is negligible. Which of the following
diagrams best represents the subsequent path of the ball?

A. B.

C. D.

(1)

5. A stone is thrown at an angle to the horizontal. Ignoring air resistance, the horizontal component of the
initial velocity of the stone determines the value of

A. range only.

B. maximum height only.

C. range and maximum height.

D. range and time of flight.

(1)

2
6. A stone is projected horizontally from the top of a cliff. Neglecting air resistance, which one of the
following correctly describes what happens to the horizontal component of velocity and to the vertical
component of velocity?

Horizontal component of velocity Vertical component of velocity

A. Decreases Increases

B. Decreases Constant

C. Constant Constant

D. Constant Increases
(1)

7. A stone is thrown with speed v from the top of a cliff of height H, as shown below.

h
v

cliff

sea

The stone is thrown at an angle to the horizontal so that it rises to a height h above the top of the cliff
before falling into the sea. The acceleration of free fall is g. Air resistance is negligible.

Which one of the following expressions gives correctly the speed of the stone as it hits the sea?

A. v+ (2 gh )
B. v+ (2 gH )
C. (2 g h + H )

D. (v 2
+ 2 gH )
(1)

3
 8. A ball rolls off a horizontal table with velocity v. It lands on the ground a time T later at a distance D from
the foot of the table as shown in the diagram below. Air resistance is negligible.

table

A second heavier ball rolls off the table with velocity v. Which one of the following is correct for the
heavier ball?

Time to land Distance from table

A. T D

B. T less than D

C. less than T D

D. less than T less than D

(1)

9. A projectile is fired from the ground at time t = 0. It lands back on the ground at time t = T. Which of the following
sketch graphs best shows the variation with time t of the vertical speed VV and horizontal speed VH of the
projectile? Air resistance is negligible.

A. B. VH
VH
speed speed

VV
VV

0 0
0 T t 0 T t
C. D.

speed speed

VH
VV VH
VV

0 0
0 T t 0 T t
(1)

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10. A particle is projected horizontally with speed v from a height H. It lands a horizontal distance R from the
point of launch as shown in the diagram below.
v

A second particle is projected horizontally from the same height with speed 2v. Neglecting air resistance
the horizontal distance travelled by this particle is

A. R.

B. 2R.

C. 2R.

D. 4R.
(1)

11. A stone is thrown from the top of a cliff with speed v at an angle θ above the horizontal, as shown.

cliff

Air resistance is negligible and the acceleration of free fall is g.

What is the horizontal velocity of the stone a time t after the stone has been thrown?

A. v sinθ

B. v sinθ – gt

C. v cosθ

D. v cosθ – gt
(1)
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12. The diagram below shows the trajectory of a ball thrown into the air. There is no air resistance.

trajectory of ball
X
A B

C
D

Which arrow gives the direction of the resultant force on the ball at the point X?

A. A

B. B

C. C

D. D
(1)13. The graph below shows the variation with time t of the velocity v of an object moving on a straight-line.

Which of the graphs below best represents the variation with time t of the acceleration a of the object?

(1)

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14. This question is about projectile motion and the use of an energy argument to find the speed with which a
thrown stone lands in the sea.

Christina stands close to the edge of a vertical cliff and throws a stone. The diagram below (not drawn to
scale) shows part of the trajectory of the stone. Air resistance is negligible.

15 m s –1
O
Q

25 m

sea

Point P on the diagram is the highest point reached by the stone and point Q is at the same height above sea
level as point O.

(a) At point P on the diagram above draw arrows to represent

(i) the acceleration of the stone (label this A).

(1)

(ii) the velocity of the stone (label this V).

(1)

The stone leaves Christina’s hand (point O) at a speed of 15 m s−1 in the direction shown. Her hand is at a
height of 25 m above sea level. The mass of the stone is 160 g. The acceleration due to gravity g = 10 m
s−2.

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(b) (i) Calculate the kinetic energy of the stone immediately after it leaves Christina’s hand.

...........................................................................................................................

...........................................................................................................................
(1)

(ii) State the value of the kinetic energy at point Q.

...........................................................................................................................
(1)

(iii) Calculate the loss in potential energy of the stone in falling from point Q to hitting the sea.

...........................................................................................................................

...........................................................................................................................
(1)

(iv) Determine the speed with which the stone hits the sea.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................
(2)
(Total 7 marks)

8
15. This question is about projectile motion.

A stone of mass 0.44 kg is thrown horizontally from the top of a cliff with a speed of 22 m s–1 as shown
below.

22 m s–1

32 m cliff

sea level

The cliff is 32 m high.

(a) Calculate the total kinetic energy of the stone at sea level assuming air resistance is negligible.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................
(3)

(b) In practice, air resistance is not negligible. During the motion of the stone from the top of the cliff to
sea level, 34 of the total energy of the stone is transferred due to air resistance. Determine the
speed at which the stone reaches sea level.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................
(2)
(Total 5 marks)

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16. This question is about the trajectory of a golf ball.

A golfer hits a golf ball at point A on a golf course. The ball lands at point D as shown on the diagram.
Points A and D are on the same horizontal level.

–1
30m s

–1
20m s
A D

The initial horizontal component of the velocity of the ball is 20 m s–1 and the initial vertical component is
30 m s–1. The time of flight of the golf ball between point A and point D is 6.0 s. Air resistance is
negligible and the acceleration of free fall g = 10 m s–2.

Calculate

(a) the maximum height reached by the golf ball.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................
(3)

(b) the range of the golf ball.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................
(2)
(Total 5 marks)

10
17. This question is about projectile motion.

A stone is projected horizontally from the top of a cliff with a speed 15 m s–1.

15 m s–1

70 m

sea

The height of the cliff is 70 m and the acceleration of free fall is 10 m s–2. The stone strikes the surface of
the sea at velocity V.

(a) Ignoring air resistance, deduce that the stone strikes the sea at a speed of 40 m s–1.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................
(2)

(b) Use your answer in (a) to calculate the angle that the velocity V makes with the surface of the sea.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................
(2)
(Total 4 marks)

11
18. This question is about projectile motion.

A ball is projected from ground level with a speed of 28 m s–1 at an angle of 30 to the horizontal as shown
below.

wall h
30
16m

There is a wall of height h at a distance of 16 m from the point of projection of the ball. Air resistance is
negligible.

(a) Calculate the initial magnitudes of

(i) the horizontal velocity of the ball;

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................
(1)

(ii) the vertical velocity of the ball.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................
(1)

(b) The ball just passes over the wall. Determine the maximum height of the wall.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................
(3)
(Total 5 marks)

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19. This question is about projectile motion.

The barrel of a rifle is held at an angle  to the horizontal. A bullet fired from the rifle leaves the barrel at
time t = 0 with a speed 200 m s–1. The graph below shows the variation with time t of the vertical height h
of the bullet.

600

500

400

h/m 300

200

100

0
0 5 10 15 20 25
t/s

(a) Using the axes below, draw a sketch graph to show the variation of h with the horizontal distance x
travelled by the bullet. (Note: this is a sketch graph; you do not have to add any values to the axes.)

x
(2)

(b) State the expression for the initial vertical component of speed Vv in terms of the initial speed of the
bullet and the angle .

...................................................................................................................................
(1)

(c) Use data from the graph to deduce that the angle  = 30. (The acceleration for free fall
g = 10 m s–2)

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 ...................................................................................................................................

...................................................................................................................................

...................................................................................................................................
(3)
(Total 6 marks)

20. This question is about projectile motion.

A ball is kicked at an angle to the horizontal. The diagram below shows the position of the ball every 0.50
s.

30

25

20

vertical displacement / m 15

10

0
0 10 20 30 40
horizontal displacement / m

The acceleration of free fall is g = 10 m s–2. Air resistance may be neglected.

(a) Using the diagram determine, for the ball

(i) the horizontal component of the initial velocity.

...........................................................................................................................

...........................................................................................................................
(1)

(ii) the vertical component of the initial velocity.

...........................................................................................................................

...........................................................................................................................
(2)

(iii) the magnitude of the displacement after 3.0 s.

...........................................................................................................................

...........................................................................................................................
(2)

(b) On the diagram above draw a line to indicate a possible path for the ball if air resistance were not
negligible.
(2)
(Total 7 marks)

14
21. This question is about projectile motion.

A stone is thrown from the top of a cliff of height 28 m above the sea. The stone is thrown at a speed of 14
m s–1 at an angle above the horizontal. Air resistance is negligible.

14 m s–1

........... 28m

sea

The maximum height reached by the stone measured from the point from which it is thrown is 8.0 m.

(a) By considering the energy of the stone, determine the speed with which the stone hits the sea.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................
(3)

(b) The stone leaves the cliff at time t = 0. It reaches its maximum height at t = TH. On the axis below,
draw a sketch-graph to show the variation with time t of the magnitude of the vertical component of
velocity of the stone from t = 0 to t = TS, the time just before the stone strikes the sea.

speed

0 t
0
TH TS
(4)
(Total 7 marks)

15
22. This question is about projectile motion.

A projectile is fired horizontally from the top of a vertical cliff of height 40 m.

projectile

cliff

40 m

sea

At any instant of time, the vertical distance fallen by the projectile is d. The graph below shows the
variation with distance d, of the kinetic energy per unit mass E of the projectile.
1400

1300

1200

E / J kg –1 1100

1000

900

800
0 5 10 15 20 25 30 35 40
d/m

(a) Use data from the graph to calculate, for the projectile,

(i) the initial horizontal speed.

...........................................................................................................................
(1)

(ii) the speed with which it hits the sea.

...........................................................................................................................
(1)

(b) Use your answers to (a) to calculate the magnitude of the vertical component of velocity with which
the projectile hits the sea.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................
(2)
(Total 4 marks)
16
23. This question is about throwing a stone from a cliff.

Antonia stands at the edge of a vertical cliff and throws a stone vertically upwards.

The stone leaves Antonia’s hand with a speed v =8.0 m s–1. Ignore air resistance, the acceleration of free
fall g is 10 m s–2 and all distance measurements are taken from the point where the stone leaves Antonia’s
hand.

(a) Determine,

(i) the maximum height reached by the stone.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................
(2)

(ii) the time taken by the stone to reach its maximum height.

.........................................................................................................................

.........................................................................................................................
(1)

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(b) The time between the stone leaving Antonia’s hand and hitting the sea is 3.0 s. Determine the height
of the cliff.

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...................................................................................................................................

...................................................................................................................................

...................................................................................................................................
(3)
(Total 6 marks)

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