Question

A stone is projected vertically upwards. When it reaches half the maximum height, its velocity is 20 m/s. What is the maximum height attained by the stone? (g 10 m/s (1) 20 m (2) 25 m (3) 30 m (4) 40

Answer 1

Given

Velocity of stone at $\dfrac{s}{2}$ is 20 m/s

To find

The maximum height attained by the stone (s).

Solution

v = Final velocity

u = Initial velocity

s = Displacement

Kinematic equations of motion have been used here

For half the maximum height we have

v = 20 m/s

$s=\dfrac{s}{2}$

$v^2-u^2=2as\\\Rightarrow 20^2-u^2=2\times-10\times\dfrac{s}{2}\\\Rightarrow u^2=400+10s$

For maximum height

v = 0

s = s

$v^2-u^2=2as\\\Rightarrow 0^2-(400+10s)=2\times -9.81\times s\\\Rightarrow -400-10s=2\times -10\times s\\\Rightarrow -400=2\times -10\times s+10s\\\Rightarrow s=\dfrac{-400}{2\times -10+10}\\\Rightarrow s=40\ \text{m}$

Maximum height reached by the stone is (4) 40 m.