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NEET2009PhysicsCenter of Mass, Momentum and CollisionActual

A ball is bouncing down a flight of stairs. The coefficient of restitution is e . The height of each step is d and the ball descends one step each bounce. After each bounce it rebounds to a height h above the next lower step. The height is large enough compared with the width of step so that the impacts are effectively head-on. Find the relationship between h and d .

Options

  1. Ah= d 1-e^2
  2. Bh= d 1+e^2
  3. Ch= d 1+e
  4. Dh= d 1-e^2

Correct answer

A. h= d 1-e^2

Step-by-step solution

The ball falls a distance h from its highest (rest) position and rebounds a distance (h-d) . Thus the coefficient of restitution e= h-d h e^2= h-d h or h= d 1-e^2

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