# Two blocks of mass 300 kg and 200 kg are moving toward eachother along a horizontal frictionless surface with velocities of and respectively. Find the final velocity of eachblock if the collision is completely elastic.

1
by ashaSabharwal

2015-10-25T17:26:50+05:30

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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

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