A man of 60 kg is running on the road and suddenly jumps into a stationary trolly car of mass 120 kg. Then, the trolly car starts moving with velocity 2 ms⁻¹. The velocity of the running man was ___________ ms⁻¹, when he jumps into the car.

Solution

Physics sir · 3 steps

Man and trolley end up moving together, so equate momentum before and after the jump.

1. Why momentum. While the man lands, the forces between him and the trolley are internal. No net horizontal external force acts, so the total horizontal momentum before equals the total after.

   m v = (m + M) V

2. Put in numbers. Before, only the man moves: 60 × v. After, man and trolley move together: (60 + 120) × 2 = 360 kg m s⁻¹.
3. So. v = 360/60 = 6 m s⁻¹, so the man was running at 6 m s⁻¹.

The common slip: 4. Using only the trolley's mass after the jump, 60 v = 120 × 2, gives 4, not 6. The man is moving too, so the mass after the jump is 180 kg.

The idea to keep. When one body jumps onto another and they move together, the final mass is the sum of both. Momentum is conserved, but kinetic energy is not.

Answer from the NTA final answer key. Solution by PrepWiser.