Question

There are two kids playing on the terrace of building of height 20 m. The first kid throws a stone up with 2 ms-1. The second kid throws a stone vertically down with same speed. What is the velocity of the stones when they reach the ground

Answer 1

The initial speed of both the stones are same. Even the stone is thrown vertically upwards or downwards, their velocity at the ground is the same.

Here the two stones are considered simultaneously.

Given,

• $\sf{u=\pm2\ m\,s^{-1}}$

because one is projected vertically upwards while the other, downwards. We consider downward motion as positive.

• $\sf{a=g=10\ m\,s^{-2}}$

Both the stones experience the acceleration due to gravity.

• $\sf{s=20\ m}$

The stones have to travel the height of the building as the displacement to reach the ground.

Then, by third equation of motion,

$\longrightarrow\sf{v^2=u^2+2as}$

$\longrightarrow\sf{v^2=(\pm2)^2+2\times10\times20}$

$\longrightarrow\sf{v^2=4+400}$

$\longrightarrow\sf{v^2=404}$

$\longrightarrow\sf{\underline{\underline{v=20.1\ m\,s^{-1}}}}$