Two objects of masses `100g` and `200g` are moving along the same line in the same direction with velocities of `2m//s` and `1m//s`, respectively. They collide and after the collison, the first object moves at a velocity of `1.67 m//s` in the same direction. Determine the velocity of the second object.

Explanation

Let the 100g and 200g objects be A and B
`therefore` Initial momentum of `A=100g times 2 ms^-1`
`=200 mg s^-1`
Initial momentum of B=`200 g times 1ms^-1`
`=200 g ms^-1`
`therefore` Total momentum of A and B before collisions
`=(200+200)g ms^-1 and =400 g ms^-1`
Let the velocity of B after collisions =v
`therefore` Momentum of B after collisions `=200g times v`
Also, momentum of A after collisions
`=100g times 1.67 ms^-1=167 g ms^-1`
`therefore` total momentum of A and B after collisions `=200g times v+167 g ms^-1`
Now , by the law of conservation of momentum
Momentum of A and B after collisions
=MoMentum of A and B after collisions
`200g times v+167 ms^-1=400 g ms^-1`
`200g times v=(400-167)g ms^-1`
`v=233/200 ms^-1=1.165 ms^-1`