Question

A body falls freely from the top of a tower. It covers $36$% of the total height in the last second before striking the ground level. The height of the tower is

• A. $50\text{m}$
• B. $75\text{m}$
• C. $100\text{m}$
• D. $125\text{m}$

Answer 1

The correct option is D $125\text{m}$

Let the height of tower be $h$ and the body takes time $t$ to reach the ground when it falls freely.
Using second equation of motion, we have
$h=ut+\frac{1}{2}g{t}^2$ (Take downward direction as positive)
$\Rightarrow h=\frac{1}{2}g{t}^2$ ($\because u=0$ during free fall) .…(i)
In the last second, i.e., in $t^{th}$ second the body travels $0.36h$. Thus, in $|t-1|$ seconds, it travels $h–0.36h=0.64h$
So, we get, $0.64h=\frac{1}{2}g(t-1{)}^2$ ....(ii)
On solving equ. (i) and (ii), we get
$\Rightarrow \frac{h}{0.64h}=\frac{\frac{1}{2}g{t}^2}{\frac{1}{2}g(t-1{)}^2}⟹t=5\text{s}$
Substituting in equation (i), $h=125\text{m}$