Question

A stone dropped from the top of a tower covers $24.5$ m in the last second of its fall. Height of the tower is

• A. $24.5m$
• B. $44.1m$
• C. $78.4m$
• D. $122.5m$

Answer 1

The correct option is B $44.1m$

Given, $u=0$

Let total time be $n$ sec.

Distance travelled in last sec:
$\Rightarrow 24.5=[\frac{\frac{1}{2}g\left(n^2\right)}{\Downarrow }-\frac{\frac{1}{2}g(n-1{)}^2}{\Downarrow }]$

(dist. travelled in $n$ secs) (dist. travelled in $(n-1)$secs)

$24.5=\frac{1}{2}g(2n-1)$

$\Rightarrow 5=2n-1$

$\Rightarrow n=3sec$

So, total height $=\frac{1}{2}g{n}^2=\frac{1}{2}g(3{)}^2=\frac{9g}{2}$$=44.1m$