Question

Two bodies of the same mass are moving with the same speed, but in different directions in a plane. They have a completely inelastic collision and move together thereafter with a final speed which is half of their initial speed. The angle between the initial velocities of the two bodies (in degree) is

Answer 1

Applying concept of momentum conservation along $x$ direction, we get
$2m{v}_0\cos \theta =2m\frac{v_0}{2}$
$\Rightarrow \cos \theta =\frac{1}{2}\text{or}\theta ={60}^{\circ }$
Hence, angle between the initial velocities of the two bodies will be, $2\theta ={120}^{\circ }$