Question

A body of mass $M,$ standing at a height h throws a ball of mass $m$ vertically down with a speed $v$. Assuming no gravity, the distance of man above the ground when ball reaches the floor is :

• A. $h$
• B. $\left(\frac{M}{M+m}\right)h$
• C. $\left(\frac{M-m}{M}\right)h$
• D. $\left(\frac{M+m}{M}\right)h$

Answer 1

The correct option is D $\left(\frac{M+m}{M}\right)h$

Using the conservation of momentum, velocity of man is given by $MV=mv$ i.e. $V=\frac{mv}{M}$ upward.

Time taken by ball to reach ground is $\frac{h}{v}$ change in the distance of man$=\left(\frac{mv}{M}\right)\frac{h}{v}=\frac{mh}{M}$

Total distance of man from ground $=h+\frac{mh}{M}=h(1+\frac{m}{M})=h\left(\frac{M+m}{M}\right)$