Question

A stone is dropped from the roof of a building takes $4\mathrm{s}$ to reach ground. The height of the building is :

• A. $19.6\mathrm{m}$
• B. $39.2\mathrm{m}$
• C. $156.8\mathrm{m}$
• D. $78.4\mathrm{m}$

Answer 1

The correct option is D

$78.4\mathrm{m}$

Step 1: Given

Initial velocity, $u=0$ (As stone is free fall)
time taken, $\mathrm{t}=4\mathrm{s}$
acceleration due to gravity, $\mathrm{g}=9.8\mathrm{m}/{\mathrm{s}}^2$
Step 2: Calculating distance covered

Using $2$nd equation of motion we get,
$\mathrm{h}=\mathrm{ut}+\frac{1}{2}g{t}^2$
$=\left(0\right)\left(4\right)+\frac{1}{2}\left(9.8\right)\left(4\right)\left(4\right)$

$=78.4\mathrm{m}$
Hence, the correct option is (D).