Question

A stone is dropped from a tower. It was found that it covered a distance of $45m$ during its last second of the fall. Calculate the time of the fall and the height of the tower? $(g=10m{s}^{-2})$

• A. $5s,45m$
• B. $10s,90m$
• C. $5s,125m$
• D. $10s,100m$

Answer 1

The correct option is C $5s,125m$

using eq of motion we have $s=ut+\left(1/2\right)g{t}^2$

$45=u\ast 1+\left(1/2\right)\ast 10\ast 1^2$

$u=45-5=40m/s$

velocity at the bottom $v^2=u^2+2gh$

$v^2={40}^2+2\ast 10\ast 45$

$v^2=2500m/s$

Height of tower $H=\frac{v^2}{2g}=\frac{2500}{2\ast 10}=125m$

time of fall $t=\frac{\sqrt{2H}}{\sqrt{g}}$$=\frac{\sqrt{2\ast 125}}{\sqrt{10}}=5sec$