Question

A stone is dropped from a certain height which can reach the ground in $5s$. If the stone is stopped after $3s$ of its fall and then allowed to fall again, then the time taken by the stone to reach the ground for the remaining distance is

• A. $2s$
• B. $3s$
• C. $4s$
• D. $8s$

Answer 1

Answer: (C)

$4s$

Let $h$ be the height, $t=5s$
$\therefore h=\frac{1}{2}g{t}^2=\frac{1}{2}\left(9.8\right)\left(25\right)=122.5m$
Distance covered in $3sec=\frac{1}{2}\left(9.8\right)(3{)}^2$
$=44.1m$
Remaining distance $=122.5-44.1=78.4m$
If $ts$ is the required time, then
$78.4=0+\frac{1}{2}g{t}^2$
$\Rightarrow t^2=\frac{784}{49}=16$
$\Rightarrow t=4s$.