Two particles with the same mass and same initial speed collide and stick together and leave the collision with half of their initial speed, bound together as one particle. What was the angle between the initial momenta of the particles before the collision?

Question

Two particles with the same mass and same initial speed collide and stick together and leave the collision with half of their initial speed, bound together as one particle. What was the angle between the initial momenta of the particles before the collision?

Answer 1

if you take the initial momentum into two perpendicular components, only the components in the direction of the final direction matter (the others add to zero).

So, each particle is at some angle Theta/2 from the line of final momentum.

finalmass*finalspeed=2m(v)cosTheta/2

2m(v/2)=2mv costheta/2

theta/2=arccos(.5)
theta=2*sixty degrees=120deg