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 figure). 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

Total time of flight of one object is $t=\frac{24\sin \theta }{g}$

$=\frac{24\sin 30°}{g}=\frac{4}{g}$

In this period both object travel 100m horizontal distance 50 m with speed $4\cos 30°$ where e = coefficient of resistution

Now $t=\frac{50}{u\cos 30°}+\frac{50}{eu\cos 30°}$

$\frac{u}{g}=\frac{50}{4\times \sqrt{\frac{3}{2}}}+\frac{50}{0.7\times \sqrt{\frac{3}{2}}4}{u}^2=g\left(100(\frac{1}{\sqrt{3}}+\frac{1}{0.7\times \sqrt{3}})\right)=100g\times 1.428u^2=1428=(37.8{)}^{2}u\approx 38.m/s$