Two perfectly elastic spheres of masses 2 kg and 3 kg moving in opposite directions with velocities `8 ms^(-1) and 6 ms^(-1)` respectively collide with each other. Find their velocities after the impact.

Explanation

Here `m_(1)=2kg, m_(2)=3kg`
`u_(1)=8ms^(-1), u_(2)=-6 ms^(-1)`
According to the law of conservation of linear momentum.
`m_(1)u_(1)+m_(2)u_(2)=m_(1)v_(1)+m_(2)v_(2)`
i.e., `(2)(8)+(3)(-6)=2v_(1)+3v_(2)`
`rArr 2v_(1)+3v_(2)=-2 " "` .....(i)
Since the collision is elastic, `u_(1)-u_(2)=v_(2)-v_(1)`
i.e., `8-(-6)=v_(2)-v_(1)`
`rArr v_(2)-v_(1)=14 " "` .....(ii)
On solving the equations (i) and (ii) we get
`v_(1)=-8.8ms^(-1), v_(2)=5.2 ms^(-1)`