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A man of 50 kg mass is standing in a gravity free space at a height of 10 m above the floor. He throws a stone of 0.5 kg mass downwards with a speed 2 m/s. When the stone reaches the floor, the distance of the man above the floor will be:

1. 9.9 m
2. 10.1 m
3. 10 m
4. 20 m

Correct answer: 10.1 m

Solution

By conservation of momentum, the man will move upwards due to the downward motion of the stone. The initial momentum is zero, so the final momentum of the man and stone system must also be zero. Using the equation m1v1 = m2v2, the man's velocity is (0.5 × 2) / 50 = 0.02 m/s upwards. The stone takes 10 / 2 = 5 seconds to reach the floor, so the man moves 0.02 × 5 = 0.1 m upwards. His final height is 10.1 m.

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