Physics - W.E.P. Question with Solution | TestHub

At the time of projection kinetic energy of the stone,

$K=\frac{1}{2}{\mathit{\text{mu}}}^2$

where m is the mass of the stone and u is the velocity of the projection

$\text{or}{u}^2=\frac{2K}{m}=\frac{2\times 98}{2}=98$

Using, v²= u²– 2gh

$\therefore h=\frac{u^2}{2\text{g}}\left(\because \text{v}=0\right)\dots \left(\text{i}\right)$

$h=\frac{98}{2\times 9·8}=5\text{m}$

$\text{Also,}K=\frac{1}{2}m\left(2\text{gh}\right)\left(\text{Using}\left(\text{i}\right)\right)$

$K^{\prime }=\frac{1}{2}m{{\text{v}}^{\prime }}^2=\frac{1}{2}m\times \left(2{\text{gh}}^{\prime }\right)$

$\therefore \frac{K^{\prime }}{K}=\frac{h^{\prime }}{h}$

According to the problem

$K^{\prime }=\frac{K}{2}$

$\frac{K}{2K}=\frac{h^{\prime }}{h}$

$h^{\prime }=\frac{h}{2}=\frac{5}{2}\text{m}=2·5\text{m}$