Question

A ball of mass in, moving with a velocity $\nu$ 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 ${\nu }_1$ What will be the velocity of the other piece?

Answer 1

Condition of the problem before and after collision are shown in following figures:
Taking components along the X-axis
$m{\nu }_2\cos \theta =m\nu ...\left(i\right)$
and taking components along the Y-axis
$m{\nu }_2\sin \theta =m{\nu }_1...\left(i\right)$
frm equation $\left(i\right)$ and $\left(ii\right)$ squaring and adding

${\nu }_2=\sqrt{{\nu }^2+{\nu }_1^2}$