Question

Two blocks of mass 300 kg and 200 kg are moving toward eachother along a horizontal frictionless surface with velocities of $50m s^{-1}$ and $100 m s^{-1}$ respectively. Find the final velocity of eachblock if the collision is completely elastic.

Answer 1

Conservation of momentum :
     200 * 100 - 300 * 50 =  200 * v1 + 300 * v2
      2 v1 + 3 v2 = 50    --- (1)

Conservation of energy :
   1/2 * 200 * v1²  + 1/2 * 300 * v2² = 1/2 * 200 * 100² + 1/2 * 300 * 50²
   2 v1² + 3 v2²  = 27, 500  --- (2)

we need to solve these equations:
   2 v1²  + 3 (50 - 2 v1)²/3²  = 27, 500
   6 v1²  + (2500 + 4 v1² - 200 v1) = 82,500
     v1² - 20 v1 - 8, 000 = 0
           v1 =   100 m/s
 => v2 =  (50 - 2 v1) / 3 = - 50 m/s