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NEETPhysicsCenter of Mass, Momentum and Collision

A boy of mass m running horizontally with a velocity v jumps onto a stationary skateboard of mass 2m . If they move together after the jump, what is the final velocity of the boy and skateboard system?

Options

  1. Av 2
  2. B2v 3
  3. Cv
  4. Dv 3

Correct answer

D. v 3

Step-by-step solution

Using the principle of conservation of linear momentum: Initial momentum of the system = Final momentum of the system The initial momentum is only due to the boy, as the skateboard is stationary: p_i = m v + (2m)(0) = m v After the jump, the boy and the skateboard move together with a common velocity v_f . The total mass is m + 2m = 3m . Final momentum: p_f = (3m) v_f Equating initial and final momentum: m v = 3m v_f v_f = v 3 Answer: v 3

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