Question

A ball, moving with speed $v$ towards north, collides with an identical ball, moving with a speed $v$ towards east. After collision the two balls stick together and move towards north-east. What will be the speed of the combination?

Answer 1

Momentum in north and east direction is conserve.Velocity toward east after collision is $v_E$

$mv=2m{v}_E{v}_E=\frac{v}{2}$

Velocity towards north is

$mv=2m{v}_N{v}_N=\frac{v}{2}$

Resultant velocity $=\sqrt{{\left(\frac{v}{2}\right)}^2+{\left(\frac{v}{2}\right)}^2}=\frac{v}{\sqrt{2}}$

North east.