Question

A body is dropped from a height $H$. The time taken to cover second half of the journey is

• A. $2\sqrt{\frac{2H}{g}}$
• B. $\sqrt{\frac{H}{g}}$
• C. $\sqrt{\frac{H}{g}}(\sqrt{2}-1)$
• D. $\sqrt{\frac{2H}{g}}\times \frac{1}{(\sqrt{2}-1)}$

Answer 1

Answer: (C)

The total time of journey
$-s=ut-\frac{1}{2}g{t}^2$
$\Rightarrow H=\frac{1}{2}g{T}^2$ ...(i)
$\frac{-H}{2}=ut-\frac{1}{2}g{t}^2$
$\Rightarrow T=\sqrt{\frac{2H}{g}}$
$\Rightarrow \frac{H}{2}=\frac{1}{2}g{t}^2$
$\Rightarrow \frac{1}{2}g{T}^2=g{t}^2(\because ut=0)$
$\Rightarrow t-\frac{T}{\sqrt{2}}$
$\Rightarrow$ Second half time $=T-t=T-\frac{T}{\sqrt{2}}$
$=T\left(1-\frac{1}{\sqrt{2}}\right)=\sqrt{\frac{2H}{g}}\left(1-\frac{1}{\sqrt{2}}\right)$
$=\sqrt{\frac{H}{g}}(\sqrt{2}-1)$