Question

A child is sitting on a swing. Its minimum and maximum heights from the ground are $0.75\text{m}$ and $2\text{m}$ respectively, its maximum speed will be

• A. $\text{15 m/s}$
• B. $\text{10 m/s}$
• C. $\text{8 m/s}$
• D. $\text{5 m/s}$

Answer 1

The correct option is D $\text{5 m/s}$

Given:
Maximum height $h=2\text{m}$
Minimum height $h_1=0.75\text{m}$
Speed at maximum height is $0\text{m/s}$
Let Maximum speed at minimum height be $V$

Apply Conservation of Mechanical Energy between maximum and minimum point

$mgh=mg{h}_1+\frac{1}{2}m{V}^2$
$V=\sqrt{2g(h-h_1)}$
$=\sqrt{2\times 10\times (2-0.75)}=5\text{m/sec}$

Hence, option $\left(B\right)$ is correct.