Question

A ball moving with velocity `2 ms^(-1)` collides head on with another stationary ball of double the mass. If the coefficient of restitution is `0.5`, then their velocities (in `ms^(-1)`) after collision will be

Answer 1

Here, `u_(1)=2m//s, u_(2)=0,m_(1)=m, m_(2)=2m`
`e=0.5, upsilon_(1)=?upsilon_(2)=?`
As `e=(upsilon_(2)-upsilon_(1))/(u_(1)-u_(2))=0.5`
`:. upsilon_(2)-upsilon_(1)=0.5(u_(1)-u_(2))=0.5(2-0)=1` …(i)
According to the law of conservation of linear momentum,
`m_(1)upsilon_(1)+m_(2)upsilon_(2)=m_(1)upsilon_(1)+m_(2)upsilon_(2)`
`m upsilon_(1)+2m upsilon_(2)=mxx2+0`
`upsilon_(1)+2upsilon_(2)=2` ..(ii)
Add (i) and (ii) `:3upsilon_(2)=3,upsilon_(2)=1m//s`
From (i), `upsilon_(1)=upsilon_(2)-1=1-1=0`