Question

A stone dropped from the top of a tower is found to travel $\frac{5}{9}$th of height of the tower during the last second of its fall. The time of fall is

• A. $2s$
• B. $3s$
• C. $4s$
• D. $5s$

Answer 1

The correct option is B $3s$

Let the stone taken $n$ second to reach the ground
Given, $u=0,a=+g$
The distance covered in $n$th second $\frac{5}{9}\times distance$ covered in $n$ seconds
$\frac{g}{2}(2n-1)=\frac{5}{9}\times \frac{g}{2}{n}^2$
$\Rightarrow 18n-9=5n^2\Rightarrow 5n^2-18n+9=0$
so, $n=3s$ or $0.6s$
But $0.6s$ time is practically not possible, hence $t=3s$