Question

A ball is dropped from rest from a height of $15\text{m}$. What is the time taken for it to reach the ground? Take $g=10\text{m}{\text{s}}^{-2}$.

• A. $\sqrt{5}\text{s}$
• B. $\sqrt{3}\text{s}$
• C. $\sqrt{2}\text{s}$
• D. $\sqrt{6}\text{s}$

Answer 1

The correct option is B $\sqrt{3}\text{s}$

Let the upward direction be positive.
Given:
The height from which the ball is dropped, $\text{h}=15\text{m}$
Hence, displacement, $s=-h=-15\text{m}$
Acceleration: $a=-g=-10\text{m}{\text{s}}^{-2}$
Since the ball is dropped from rest, initial velocity, $\text{u}=0$

Using the second equation of the motion:
$\text{s}=\text{ut}+\frac{1}{2}{\text{at}}^2$
$-15=0+\frac{1}{2}\times \text{-10}\times {\text{t}}^2$
$⟹\text{t}=\sqrt{3}\text{s}$