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  4. In gravity-free space, a man of mass M standing at a height h above the floor throws a ball of mass m straight down with a speed u . When the ball reaches the floor, the distance of the man above the floor will be

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Q. In gravity-free space, a man of mass $M$ standing at a height $h$ above the floor throws a ball of mass $m$ straight down with a speed $u$ . When the ball reaches the floor, the distance of the man above the floor will be

NTA AbhyasNTA Abhyas 2022

Solution:

Due to conservation of momentum in the vertical direction, the man will begin to move up with speed $\frac{m u}{M}$ . The ball will reach the floor in time $ \, \frac{h}{u}$ . In this time the man will move up by $\left(\frac{m u}{M}\right) \, \left(\frac{h}{u}\right)$ . Total distance of man from floor $=h \, + \, \frac{m h}{M}$ .