Question : A ball is released from the top of a tower of height h metres. It take T seconds to reach the ground. What is the position of the ball is T/3 seconds?
(a) 8h/9 metres from the ground.
(b) 7h/9 metres from the ground.
(c) h/9 metres from the ground.
(d) 7h/18 metres from the ground.
Solution :
Case I
u=0 m/s
s=h
t=T
a=g
s=ut+½at²
h=(0)t+½gT²
h=½gT² — (1)
Case II
u=0 m/s
s=?
t=T/3
a=g
s=ut+½at²
s=(0)t+½g(T/3)²
s=½g[T²/9]
s=[½gT²]/9
s=h/9 [Using equation (1)]
Position of the ball from the bottom of the ground
= h-h/9
= [9h-h]/9
= 8h/9
Hence, after T/3 seconds the ball will be at a height of 8h/9 metres from the ground.
So, (a) 8h/9 metres from the ground, would be the correct option.