A body of mass m makes an elastic collision with another identical body at rest.Show that if the collision is not head-on,the bodies go at right angle to each other after the collision.
Since it is not a head on collision,the two bodies move in different dimensions.
Let v1,v2→ velocities of the bodies vector collision.
Since,the collision is elastic,applying law of conservation of momentum on X=direction
mu1+m×0=mv1 cos α+mv1 cos β
⇒v1 cos α+v2 cos β=u1 ...(i)
Putting law of conservation of momentum in y direction O=mv1 sin α v2 sin β ...(ii)
Again (12)mu21+0=(12)mv21+(12)m×v22
⇒u21=v21+v22 ...(iii)
Squaring equation (i)
v21+v22=v21 cos2 α+v22 cos2 β+2v1v2 cos α cos β
⇒v21 sin2 α+v22 sin2 β+2v1v2 cos α cos β
⇒2v21sin2α=2×v1×v1 sin αsin β cos α cos β
⇒ sin α sin β= cos α cos β
⇒ cos α. cos β− sin α cos β
⇒cos(α+β)=0=cos 90∘
⇒α+β= 90∘