1. This question is about projectile motion.
A stone is thrown horizontally from the top of a vertical cliff of height 33 m as shown below. 1 8 m s – 1
3 3 m
s e a l e v e l
The initial horizontal velocity of the stone is 18 m s–1 and air resistance may be assumed to be
negligible.
(a) State values for the horizontal and for the vertical acceleration of the stone.
Horizontal acceleration: ... Vertical acceleration: ...
(2)
(b) Determine the time taken for the stone to reach sea level.
... ... ...
(2)
(c) Calculate the distance of the stone from the base of the cliff when it reaches sea level.
... ...
2. 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. 2 2 m s– 1
c l i f f 3 2 m
s e a l e v e l
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.
... ... ...
3. 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.
A D
3 0 m s
2 0 m s– 1 – 1
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.
... ... ...
4. This question is about projectile motion.
A stone is projected horizontally from the top of a cliff with a speed 15 m s–1.
7 0 m
1 5 m s– 1
s e a
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.
... ... ... ...
5. 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.
w a l l h
1 6 m 3 0
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.
... ... ... ... ...
6. 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 thebarrel 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.
6 0 0
5 0 0
4 0 0
3 0 0
2 0 0
1 0 0
0
2 5 2 0
1 5 1 0
5 0
h / m
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.)
h
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
....
(c) Use data from the graph to deduce that the angle
= 30. (The acceleration for free fall g = 10 m s–2)... ... ... ...
(3) (Total 6 marks)
7. 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.
5 3 0
2 5
2 0
1 5
1 0
1 0 2 0 3 0 4 0
h o r i z o n t a l d i s p l a c e m e n t / m 0
0 v e r t i c a l d i s p l a c e m e n t / 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.
... ...
(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)
8. 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.
. .
.
. .
.
. .
.
. .
2 8 m
s e a 1 4 m s– 1
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.
... ... ... ...
(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.
s p e e d
0 0
T
H T St
9. This question is about projectile motion.
A projectile is fired horizontally from the top of a vertical cliff of height 40 m.
c l i f f
s e a p r o j e c t i l e
4 0 m
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.
E / J k g
1 4 0 0
1 3 0 0
1 2 0 0
1 1 0 0
1 0 0 0
9 0 0
8 0 0
d / m
0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0
(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.
... ... ...
10. 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)
(b) The time between the stone leaving Antonia’s hand and hitting the sea is 3.0 s. Determine
the height of the cliff.
