Question

A particle of mass m moving at 5.0 m/s in the positive x direction makes a glancing elastic collision with a particle of mass 2m that is at rest before the collision. After the collision, m moves off at an angle of 45

Answer 1

In x direction linear momentum is: before = m *5 = after = m v_m cos60 + 2m v_2m cos45^o
In y direction initial linear momentum as well as final is zero.    m v_m sin60 - 2m v_2m sin45^o = 0
from y direction:   v_2m = (m v_m sin60)/(2m sin45^o) = 0.612 v_m
and use it in x direction: m *5 = m v_m cos60 + 2m (0.612 v_m) cos45^o
and factoring:   v_m = 5 / [cos60 + 2*0.612*cos45]

= 5 / 0.865 = 5 / 0.5 + 1.224 * 0.707 = 5 / 1.365 = 3.661 m/s