Question

A ball of mass $2kg$ is thrown vertically upwards by applying a force by hand. If the hand moves $0.2m$ while applying the force and the ball goes upto $2m$ height further, find the magnitude of the force. ($g=10m{s}^{-1}$)

Answer 1

Let the ball starts moving with velocity $u$ and it reaches up to a max height $H_{max}$

From $H_{max}=\frac{u^2}{2g}$

$u=\sqrt{H_{max}\times 2g}$

$u=\sqrt{2\times 10\times 2}=2\sqrt{1}0m/s$

This velocity is supplied to the ball by the hand and initially the hand was at rest, it acquires this velocity in distance of 0.2m

$\therefore a=\frac{u^2}{2S}=\frac{(2\sqrt{1}0{)}^2}{2\times 0.2}=100m/s^2$

So upward force on the wall is

$F=m(g+a)=2(10+100)=220N$