Question

A body falls freely from a tower and travels a distance of $40$ in its last two seconds. The height of the tower is

• A. $54\text{m}$
• B. $45\text{m}$
• C. $80\text{m}$
• D. $65\text{m}$

Answer 1

The correct option is B $45\text{m}$

Let the body fall through the height of the tower in $t$ seconds.
From equation of motion we have
$S=ut+\frac{1}{2}g{t}^2$ , here u= 0 as the body is free falling
$H=\frac{1}{2}g{t}^2$
Where $H$ is the height of the tower. The distance covered by the body in $t-2$ seconds is $H^{\prime }=\frac{1}{2}g(t-2{)}^2$
Now, according to question $H–H\text{'}=40\text{m}$
Assuming $g$ as $10{\text{m/s}}^2$
$t^2–(t–2{)}^2=8$
$4(t–1)=8$
$t=3\text{seconds}$
Now, the height of tower
Therefore, option B is correct.