Page 8 - Pra U STPM 2021 Penggal 1 - Physics

Physics Term 1 STPM Chapter 2 Kinematics
8. Figure 2.3 shows a particle being projected upwards from the point A. It reaches the highest point
E and then falls down to a point below A.

Example 3

A bullet is fired vertically upwards from the ground with an initial velocity of u and takes a time 2
of t 1 to reach a point P at a height h. From then the bullet takes a further time of t 2 to move to the
highest point and back to the ground. Find in terms of t 1 , t 2 and g
(a) the initial velocity u,
(b) height h, and
(c) the greatest height H reached.
Solution:

(a) Assume the upwards direction as positive, then a = –g. H
Total time taken for the bullet to move up and back to the ground,
t = (t 1 + t 2 ) P
When the bullet returns to the ground, H v t 1
displacement, s = 0
h
1
Using s = ut + at 2
2 (t + t )
1
2
1
0 = u(t 1 + t 2 ) – g(t 1 + t 2 ) 2
2
1
u = g(t 1 + t 2 )
2
(b) When s = h, t = t 1 (c) At the highest point, s = H, velocity = 0
2
Using v = u + 2as
2
1
Using s = ut + at 2
2 0 = u – 2gH
2
1 1
2 u = g(t 1 + t 2 )
2 2 u 2 1
h = ut 1 – gt 1
H = u = g(t 1 + t 2 )
2
1 1 2g
= 2
2 g(t 1 + t 2 )t 1 – gt 1 1 1 ] 2
2
= g(t 1 + t 2 )
1 2g[ 2
=
2 gt 1 t 2
1
= g (t 1 + t 2 ) 2
8
Quick Check 2
1. A ball is thrown vertically upwards from the 2. A spaceship descends at a constant velocity
top of a building, 9.0 m above the ground with of 10 m s on the moon. When it is 120 m
–1
a speed of 8.0 m s . The ball hits the ground from the moon’s surface, an object falls off the
–1
after a time T. Calculate spaceship. If the acceleration due to gravity on
(a) the time taken to reach the greatest height. the moon is 1.6 m s , what is the velocity of the
–2
(b) the greatest height reached by the ball. object when it reaches the surface of the moon?
(c) the time, T taken by the ball to reach the
ground.
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02 STPM PHY T1.indd 37 4/9/18 8:19 AM