A cube of mass m slides without friction at a speed vo. It undergoes a perfectly elastic collision with the bottom tip of a rod length d and mass 2m. The rod is pivoted about a frictionless axle through its center, and initially it hangs straight down and is at rest. What is the cube's velocity- both speed and direction after the collision?
Moment of inertia for rod pivoted about center I=(1/12)mr^2
The Attempt at a Solution
I used conservation of energy
Kcubeinitial = Krotational of rod + Kcubefinal
I replaced angular velocity with v1/.5d
.5mvo^2 = .5mvf^2 + .5(1/12)2md^2 * (v1/.5)^2
Then I used conservation of momentum:
mvo= mvf + 2mv1
But substituting these two equations into each other leads to something I can't solve. Should I try angular momentum?