A child is swinging a swing. Minimum and maximum heights of swing from earths surface are 0.75 m and 2m respectively. The maximum velocity of this swing is:

Key Idea: Maximum kinetic energy of swing should be equal to difference in potential energies to conserve energy. From energy conservation $ \frac{1}{2}mv_{\max }^{2}=mg({{H}_{2}}-{{H}_{1}}) $ Here, $ {{\text{H}}_{\text{1}}}\text{=} $ maximum height of swing from earths surface $ =0.75\,m $ $ {{H}_{2}}= $ maximum height of swing from earths surface $ =2\,m $ $ \therefore $ $ \frac{1}{2}mv_{\max }^{2}=mg(2-0.75) $ or $ {{v}_{\max }}=\sqrt{2\times 10\times 1.25}=\sqrt{25}=5\,m/s $