Question

A body. dropped from a height $ h $ at time $ t=0 $ reaches the ground at tune $ {{t}_{0}}. $ would have reached a height $ h/2 $ at time:

• A. $ \frac{{{t}_{0}}}{2} $
• B. $ \frac{{{t}_{0}}}{\sqrt{2}} $
• C. $ t_{0}^{2} $
• D. $ \frac{1}{t_{0}^{2}} $

Answer 1

Answer: (B)

We have, $ h=\frac{1}{2}gt_{0}^{2} $ ...(i)
Let $ {{t}_{1}} $ be the time taken by the body to reach a / height $ \frac{h}{2}. $ Then
$ \frac{h}{2}=\frac{1}{2}gt_{1}^{2} $
$ \Rightarrow $ $ \frac{1}{4}gt_{0}^{2}=\frac{1}{2}gt_{1}^{2} $ [from (i)]
$ \Rightarrow $ $ {{t}_{1}}=\frac{{{t}_{0}}}{\sqrt{2}} $