Mass m1, moving to the right, collides with mass m2, which is at rest before the collision. The masses are m1 = 0.1 kg and m2 = 0.2 kg. The scattering angle of m1 will be 30 degrees above the horizontal.
a) Calculate the recoil angle phi of m_2.
b) Calculate the recoil speed of m_2.
m_1*v_0 = m_2*v_2*cosφ + m_1*v_1*cos30 (mom. cons. in x)
m_2*v_2*sinφ = m_1*v_1*sin30 (mom. cons. in y)
0.5*m_1*v_0^2 = 0.5*m_1*v_1^2 + 0.5*m_2*v2^2 (KE cons.)
The Attempt at a Solution
I'll spare you the messy algebra unless requested. My approach has been to try to eliminate variables, since I have FOUR unknowns (v_0, v_1, v_2, and phi) and only 3 equations. But nothing I've done so far has helped me. Can I really come up with formulas for v_2 and phi in terms of just m_1, m_2, and the 30 deg recoil angle of m_1?
I have also considered trying to use the c.m. frame, but I really don't see how that would help in this problem.
It seems to me the physics here is simple. It's the algebra that's messing me up! Maybe? Can anyone offer a friendly nudge in the right direction?