Question

A boy 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

Answer: (D)

$\left( \frac{M + m}{M} \right)h$

Answer 2

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 is the distance of man = $\left( \frac{mv}{M} \right)\frac{h}{v} = \frac{mh}{M}$

Total distance of man from ground = h + $\frac{mh}{M}$

= $\left( 1 + \frac{m}{M} \right) = h\left( \frac{M + m}{M} \right)$