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.


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