If an object ms 40 kg Elastically collides with another obje

If an object m_s 40 kg Elastically collides with another object M_2 = 30 kg which happens to be intially at rest, what would be the velocity of M_1 before and after the collision?

Solution

v1i = v(cos30i + sin30j) = 0.866vi + 0.5v j

v2i = 0

v1f = v1 ( cos60i + sin60j )   = 0.5v1 i + 0.866v1 j m/s

v2f = 10 ( - sin25i - cos25 j ) = - 4.23i - 9.06j m/s

Applying momentum conservation,

m1 v1i + m2 v2i = m1 v1f + m2 v2f

40 ( 0.866vi + 0.5 v j) + 0 = 40 ( 0.5v1 i + 0.866v1 j) + (30 (-4.23i - 9.06 j ))

3.464Vi + 2Vj = 2v1 i + 3.464v1 j - 12.69i - 27.18j

(2 v1 - 3.464v)i + (3.464v1 - 2 v ) = 12.69i + 27.18j

2 v1 - 3.464v = 12.69

3.464v1 - 2 v = 27.18

v1 = 8.6

v = 1.3

v1i = v = 1.3 m/s

v1f = v1 = 8.6 m/s

{ in practical. this can not happen. Im figure you has shown that m2 is moving to the left
after collision, m2 must move toward right (in elastic collision ))