Question

A child is swinging a swing. Minimum and maximum heights of swing from earth's surface are $0.75\, m$ and $2 \,m$ respectively. The maximum velocity of this swing is

• A. 5 m/s
• B. 10 m/s
• C. 15 m/s
• D. 20 in/s

Answer 1

Answer: (A)

5 m/s

Answer 2

Maximum kinetic energy of swing should be equal to difference in potential energies to conserve energy. From energy conservation $\frac{1}{2} m v_{\max }^{2}=m g\left(H_{2}-H_{1}\right)$ Here, $H_{1}=$ minimum height of swing from earth's surface $=0.75\, m$ $H_{2}=$ maximum height of swing from earth's surface $=2 \,m$ $\therefore \frac{1}{2} m v_{\max }^{2}=m g(2-0.75)$ or $v_{\max }=\sqrt{2 \times 10 \times 1.25}$ $=\sqrt{25}=5 \,m / s$