Question

A ball of mass $m$ falls vertically to the ground from a height $h_1$ and rebound to a height $h_2$. The change in momentum of the ball on striking ground is :

• A. $mg(h_1-h_2)$
• B. $m(\sqrt{2g{h}_2}+\sqrt{2g{h}_1})$
• C. $m\sqrt{2g(h_1+h_2)}$
• D. $m\sqrt{2g}(h_1+h_2)$

Answer 1

The correct option is B $m(\sqrt{2g{h}_2}+\sqrt{2g{h}_1})$

Velocity just before striking the ground will be velocity gained after falling a height $h_1$ so $V_i=\sqrt{2g{h}_1}$

Velocity just after rebounding will be the velocity $needed$ to gain a height $h_2$ so $V_f=\sqrt{2g{h}_2}$

so change in momentum will be $\Delta P=m\Delta V=m(V_f-V_i)=m(\sqrt{2g{h}_2}+\sqrt{2g{h}_1})$