A particle of mass m1 =2.8 kg moving along the x axis collides with a particle of mass m2 = 5 kg initially at rest. The incoming particle is deflected in the direction 23 degrees above the x axis, whereas the target particle moves off at 14 m/s at 39 degrees below the x axis. What are the initial and final speeds of the 2.8 kg particle?

Question

A particle of mass m1 =2.8 kg moving along the x axis collides with a particle of mass m2 = 5 kg initially at rest. The incoming particle is deflected in the direction 23 degrees above the x axis, whereas the target particle moves off at 14 m/s at 39 degrees below the x axis. What are the initial and final speeds of the 2.8 kg particle?

Answer 1

conserve momentum. If the incoming particle has velocity v0 i, and leaves with speed v1, then we have

2.8 * v0 i = 2.8 * v1 cos23° i + 2.8 * v1 sin23° j + 5*14 cos39° i - 5*14 sin39° j
equating the i and j parts,
2.8 v0 = 2.577 v1 + 54.4
0 = 1.094 v1 - 44.052

now just solve for v0 and v1