Show that two equal masses undergo oblique elastic collision will move at right angles after collision , if the second body initialyy at rest .

Explanation

Consider two bodies possess equal mass (m) and they undergo oblique collision .
Let the first body moving with initial velocity 'u' collides with the second body at rest .

In elastic collision , momentum is conserved . So , conservation of momentum along X-axis yields .
`"mu"=mv_(1)costheta_(1)+mv_(2)costheta_(2)`
(i.e.)`u=v_(1)costheta _(1)+v_(2)costheta _(2)" " ...(1)`
along Y-axis
`0=v_(1)sintheta _(1)-v_(2)sintheta _(2)" " ...(2)`
squaring and adding eq . (1) and (2) we get `u^(2)=v_(1)^(2)+v_(2)^(2)+2v_(1)v_(2)cos(theta_(1)+theta_(2)) " " ...(3)`
As the collision is elastic ,
Kinetic Energy (k.E) is also conserved .
(i.e.) `(1)/(2)"mu"^(2)=(1)/(2)mv_(1)^(2)+(1)/(2)mv_(2)^(2)`
`rArru^(2)=v_(1)^(2)+v_(2)^(2)" " ...(4)`
From eq . (3) and (4) `2v_(1)v_(2)cos(theta_(1)+theta_(2))=0`
As it is given that `v_(1)ne0andv_(2)ne0`
`thereforecos(theta_(1)+theta_(2))=0" or "theta_(1)+theta_(2)=90^(@)`.
The two equal masses undergoing oblique elastic collision will move at right angles after collision will move at right angles after collision , if the second body initially at rest .