Question

2 stones are thrown vertically upwards simultaneously with their initial velocity u1 & u2. Prove that the heights reached by them would be in the ratio u1 square : u2 square. Assume that upward acceleration is -g and downwards acceleration is +g

Answer 1

The distance reached by the stones with velocity u₁ and u₂ is their maximum height.
Hmax=u²/2g
Hmax for the stone with velocity u₁=u₁²/-2g=-u₁²/2g
Hmax for the stone with velocity u₂=u₂²/-2g=-u₂²/2g
Ratio=-u₁²/2g/-u₂²/2g=u₁²/u₂²=u₁²:u₂²