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A 2 ~kg ball moving at 24 ~ms ⁻¹ undergoes inelastic head-on collision with a 4 ~kg ball moving in the opposite direction at 48 ~ms ⁻¹ . If the coefficient of restitution is 2 / 3 , their velocities in ms ⁻¹ after impact are

Options

  1. A-56,-8
  2. B-28,-4
  3. C-14,-2
  4. D-7,-1

Correct answer

A. -56,-8

Step-by-step solution

aligned & aligned & v₁^ = [ m₁-e m₂ m₁+m₂ ] v₁- [ (1+e) m₂ m₁+m₂ ] v₂ &= [ 2- ( 2 3 ) 4 2+4 ] 24- [ (1+ 2 3 ) 4 2+4 ] 48 &=-56 ~m / s & and v₂^ = [ (1+e) m₁ m₁+m₂ ] v₁- [ m₂-e m₁ m₁+m₂ ] v₂ &= [ (1+ 2 3 ) 2 2+4 ] 24- [ 4- ( 2 3 ) 2 2+4 ] 48 &=-8 ~m / s aligned aligned

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