Topic 8.7
8
Projectile motion 1
Projectiles
Aims
In this activity you will interpret the motion of falling balls and show whether you understand
the three key principles of projectile motion in Topic 8.7 and the equations for constant
acceleration in Topic 8.6 of your textbook. You will then predict the effect of air resistance
on projectile motion.
Two-dimensional motion
The graph below shows the positions of two balls. Ball 1 falls vertically from rest, while
ball 2 starts with an initial sideways velocity before it falls. Successive positions of each ball
are shown every 0.1 s. Thus ball 1 starts at 0 s and 0.1 s later has fallen almost 0.05 m while
ball 2 has also travelled 0.2 m horizontally in that time.
1 Explain why successive images of ball 1 are further apart.
2 What feature of the graph shows that ball 2 has a constant horizontal velocity?
3 What feature of the graph shows that the vertical velocity of ball 2 is unaffected by its
movement horizontally?
4 On the graph, draw the position of a third ball which is launched sideways with a
horizontal velocity of 1.0 m s−1. You should draw the position of this ball every 0.1 s.
5 Calculate the following:
(a) The horizontal velocity of ball 2
AQA Physics A AS Level Extension Activity © Nelson Thornes Ltd 2008
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Topic 8.7
8
Projectile motion 1
(b) The vertical velocity of ball 1 after 0.50 s
(c) The vertical acceleration of ball 1
(d) The horizontal acceleration of ball 2
(e) The resultant velocity of ball 2 after 0.50 s (Remember: velocity is a vector and the
answer needs a direction. Hint: you may need to draw a vector diagram to add
vertical and horizontal velocities.)
6 The graph was drawn assuming only the force of gravity acts on the two balls. In real life
air resistance will also act on the two balls.
What difference does air resistance make to the position of the balls shown in the graph?
AQA Physics A AS Level Extension Activity © Nelson Thornes Ltd 2008
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Topic 8.7
8
Projectile motion 1
Projectiles
Aims

To interpret the motion of falling balls.

To show an understanding of the three key principles of projectile motion in Topic 8.7.

To show an understanding of the equations for constant acceleration in Topic 8.6.

To predict the effect of air resistance on projectile motion.
Teaching notes
Students will need to be shown the figures in Topic 8.7 and have projectile motion explained.
Students may use their common sense to predict what happens when air resistance is included
but they may wish to consult Topic 9.3 of the textbook for more information.
Answers
7 Vertical velocity increases as the ball accelerates downwards due to the force of gravity.
8 Successive positions of ball 2 are the same distance apart horizontally, 0.2 m.
9 The vertical position of ball 2 is exactly the same as ball 1 proving that its sideways
velocity has not altered how far it has fallen vertically.
10 Successive positions of the ball should be 0.1 m apart, i.e. midway between ball 1 and
ball 2 at the heights shown.
11 (a) speed =
distance
0 .2
=
= 2.0 m s−1
time
0 .1
1
(u + v)t vertically, and knowing that u = 0 because the ball started from
2
2 s 2  1 .2
rest, gives v 
=
(accept s between 1.2 m and 1.3 m at 0.5 s)
t
0 .5
So, v = 4.8 m s−1
(f) Using s =
(g) a =
(v  u ) 4.8
=
(or student’s value from (b))
0.5
t
a
So, a = 9.6 m s−2
(h) zero
(i) (resultant velocity)2 = (horizontal velocity)2 + (vertical velocity)2 = 22 + 4.82
resultant velocity = 5.2 m s−1
 vertical velocity 

angle to horizontal = tan−1 
 horizontal velocity 
= 67°
12 For ball 1, when the drag force due to air resistance matches the downward force on the
ball due to gravity, the ball will fall at constant velocity, and successive positions on the
AQA Physics A AS Level Extension Activity © Nelson Thornes Ltd 2008
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Topic 8.7
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Projectile motion 1
graph will be the same distance apart.
For ball 2, air resistance will cause the ball to decelerate horizontally until it has no
horizontal velocity. It will then be falling vertically and, as with ball 1, will reach a
constant downward velocity when the drag force due to air resistance matches the
downward force due to gravity. Successive positions on the graph vertically will then be
the same distance apart.
In the same time interval the balls will have moved less far when compared with their
motion ignoring air resistance. This means that they will appear closer together on the
graph.
AQA Physics A AS Level Extension Activity © Nelson Thornes Ltd 2008
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