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.
As it is not a head on collision, the two bodies move in different dimensions.
Initial velocity of 1st body is u1 and 2nd body is u2=0 (as it is in rest).
Let v1 and v2 are the velocities of the bodies after collision.
Since the collision is elastic
According to law of conservation of momentum (in x direction)
________ (1)
Putting law of conservation of momentum in y direction
_________ (2)
By law of conservation of energy
__________ (3)
Squaring equation (1)
Equating the above equation with equation (3)
From equation (2)
So, it is proven that the collision is not head-on, the bodies go at right angle to each other after the collision.