Question

A body dropped freely from the top of a tower travels $44.1$m in the last second of its fall. The total height of the tower is?

• A. $1.225$m
• B. $12.25$m
• C. $1225$m
• D. $122.5$m

Answer 1

Answer: (D)

$122.5$m

Given,

$g=9.8m/s^2$

$h=44.1m$

$t=1sec$

By 2nd equation of motion,

$s=ut+\frac{1}{2}g{t}^2$

$44.1=u\left(1\right)+\frac{1}{2}\times 9.8\times (1{)}^2$

$44.1=u+4.9$

$u=39.2m/s$ (final velocity)

From 3rd equation of motion,

$2gH=v^2-u^2$ (initial velocity is zero)

$H=\frac{39.2\times 39.2}{2\times 9.8}=78.4m$

Height of the tower,

$H_t=H+h=78.4+44.1=122.5m$

The correct option is D.