Question

​Obtain expressions for velocities of the two bodies after head on elastic collision.

Answer 1

Dear Student,

mas of two bodies be M and m and velocity be V and v respectively.

let suppose velocity after collision be V'and v'

by applying momentum conservation

$$\begin{gathered} MV-mv=MV\text{'}+mv\text{'}............1 \\ energywillalsoconservedascollisioniselastic \\ \frac{M{V}^2}{2}+\frac{m{v}^2}{2}=\frac{MV{\text{'}}^2}{2}+\frac{mv{\text{'}}^2}{2}...........2 \\ byu\sin gsubsitutionmethodwecanfindV\text{'}andv\text{'} \\ V\text{'}=\frac{M-m}{M+m}V-\frac{2m}{M+m}v \\ v\text{'}=\frac{2M}{M+m}V+\frac{M-m}{M+m}v \\ Regards \end{gathered}$$