Question

Two objects of the same mass and with the same initial speed, moving in a horizontal plane, collide and move away together at half their initial speed after the collision. The angle (in degree) between the initial velocities of the objects is

Answer 1

Initial angle between the velocities is $2\theta$ and after the collision, combined mass moves along the bisector line.

Conserving momentum along final direction of motion,
$2mv\cos \theta =2m\frac{v}{2}$
$\Rightarrow \cos \theta =\frac{1}{2}$
$\Rightarrow \theta ={60}^{\circ }$
So, angle between initial velocities of the object $=2\theta ={120}^{\circ }$
Final answer: $120°$