Object A has a mass of 2.0 kg and an initial velocity of 2.5 m/s. It strikes Object B, which is at rest and has a mass of 2.0 kg as well.
After the collision, the objects travel in different directions, with Object B travelling at an angle of 44 degrees from its original position.
What is the velocity of Object B after the collision and what is the displacement angle of Object A from the point of collision?
Momentum before collision = momentum after collision
Px = (m1 * vf1 * cosX) + (m2 * vf2 * cosY)
Py = (m1 * vf1 * sinX) + (m2 * vf2 * sinY)
KE before collision = KE after collision
KEf = (.5)(m1)vf12 + (.5)(m2)vf22
The Attempt at a Solution
I first calculated the components of momentum and kinetic energy before impact.
Px = 2 kg * 2.5 m/s = 5.0 kg*m/s
Py = 0 kg*m/s
KE = .5 * 2 kg * 2.5 m/s = 6.25 J
Then, I setup equations relating the objects post-impact to the momentum and energy they should have.
5 = 2*vf1*cosX + 2*vf2*cos44
0 = 2*vf1*sinX + 2*vf2*sin44
6.25 = vf12 + vf22
I've tried using substitution to solve for one of the variables, but each time I end up getting arcsines within cosines equaling sines. And I really don't know how to solve from there.
Am I at least on the right track? Should I solve for the angle first? Does it matter?