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)`
`rArr2v_(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) = - 8.8 ms^(-1), v_(2) = 5.2 ms^(-1)`