A lighter body collides with much more massive body at rest. Prove that the direction of lighter body is reversed and massive body remains at rest.

Explanation

Since the first body is very much lighter than the second body `(m_(1)ltltm_(2),(m_(1))/(m_(2))ltlt1)`, the ratio `(m_(1))/(m_(2))~~0` and also if the target is at rest `(u_(2)=0)`
Dividing numerator and denominator of equation `v_(1)=((m_(1)-m_(2))/(m_(1)+m_(2)))u_(1)+((2m_(2))/(m_(1)+m_(2)))u_(2)` by `m_(2)`, we get
`v_(1)=(((m_(1))/(m_(2))-1)/((m_(1))/(m_(2))+1))u_(1)+((2)/((m_(1))/(m_(2))+1))(0)`
`v_(1)=((0-1)/(0+1))u_(1)" "[(m_(1))/(m_(2))=0]`
`v_(1)=-u_(1)'`
Similarly, dividing numerator and denominator of equation `v_(2)=((2m_(1))/(m_(1)+m_(2)))u_(1)+((m_(2)-m_(1))/(m_(1)+m_(2)))u_(2)`,
by `m^(2)`, we get
`v_(2)=((2(m_(1))/(m_(2)))/((m_(1))/(m_(2))+1))u_(1)+((1-(m_(1))/(m_(2)))/((m_(1))/(m_(2))+1))(0)`
`v_(2)=(0)u_(1)+((1-(m_(1))/(m_(2)))/((m_(1))/(m_(2))+1))(0)`
`v_(2)=0`