Question

A stone is dropped from a certain height which can reach the ground in 8 sec . It is stopped after three seconds of its fall and then is again released. The total time taken by the stone to reach the ground will be ( $g=10m/s^2$ )

• A. 9.6 s
• B. 10.2 s
• C. 10.4 s
• D. 11.4 s

Answer 1

Answer: (C)

Height from which the stone is dropped
$h=\frac{1}{2}g{t}^2=\frac{1}{2}\times 10\times 8^2=320m$
The distance of fall of stone for 3 seconds
$h_1=\frac{1}{2}\times 10\times 3^2=45m$
The remaining distance for the falling stone
$=320-45=275m$
If $t^{\prime }$ is the time taken to fall the distance 275 m , then
$t^{\prime }=\sqrt{\frac{2\times 275}{10}}=\sqrt{55}=7.416s=7.4s$
Total time $=3+7.4=10.4s$