Question

Two identical smooth balls are projected from points O and A on the horizontal ground with same speed of projection. The angle of projection in each case is ${30}^o$(See Fig,). The distance between O and A is $100$m. The balls collide in mid-air and return to their respective points of projection. If the coefficient of restitution is $0.7$, find the speed of projection of either ball(in m/s) correct to nearest integer.(Take $g=10m{s}^{-2}$ and $\sqrt{3}=1.7$).

Answer 1

The collision does not alter the vertical component of the velocity of either ball so, $t_1+t_2=T$

$\frac{50}{ucos30}+\frac{50}{0.7ucos30}=\frac{2usin30}{10}\frac{50\times 2}{u\sqrt{3}}+\frac{50\times 2}{0.7u\sqrt{3}}=\frac{2u\times 0.5}{10}\frac{70+100}{0.7u\sqrt{3}}=\frac{u}{10}{u}^2=\frac{170\times 10}{0.7\times 1.7}u=\sqrt{\frac{1000}{0.7}}u\approx 38m/s$