A ball of mass m moving with a velocity v along X-axis, strikes another ball of mass 2m kept at rest. The first ball comes to rest after collision and the other breaks into two equal pieces. One of the pieces starts moving along Y-axis with a speed `v_1`. what will be the velocity of the other piece?

Explanation

The total linear momentum of the baslls before the collision is mv along the X-axis After the colision, momentum of the first ball=0, momentum of the first piece `=mv_1` along the Y-axis and momentum of the second piece `=mv_2` along its direction of motion where `v_2` is the speed of the second piece. These three should add to mv along the X-axis, which is the initial momentum of the system.

Taking components along the X-axis,
`mv_2costheta=mv`...i
and taking components along the Y-axis
`mv_2sintheta=mv_1`..........ii
From i and ii
`v_2=sqrt(v^2+v_1^2) and thantheta=v_1/v`.