Hi there!
Since the collision is elastic, we must also satisfy the following condition:
Ei = Ef, or:
KEi = KEf
Begin by writing an expression for momentum. (p = mv) Remember that one ball's direction is negative; in this instance, we can let the second ball be moving LEFT.
mv1 + mv2 = mvf1 + mvf2
0.220(1.84) + 0.220(-.530) = 0.220(vf1 + vf2)
0.2882/0.220 = vf1 + vf2
1.31 = vf1 + vf2
Now, we can express this as a conservation of energy:
1/2mv1² + 1/2mv2² = 1/2mvf1² + 1/2mvf2²
Plug in values and simplify:
0.403315 = 1/2m(vf1² + vf2²)
Simplify further:
3.6665 = vf1² + vf2²
Use the equation derived from momentum above and solve for one variable:
vf2 = 1.31 - vf1
Plug in this expression for vf2:
3.6665 = vf1² + (1.31 - vf1)²
Expand:
3.6665 = vf1² + 1.7161 - 2.62vf1 + vf1²
Simplify:
1.9504 = -2.62vf1 + 2vf1²
Solve for vf1 using a graphing calculator:
vf1 = -0.53 m/s or 1.84 m/s; we must figure out which one is correct.
Since v1 is heading to the right initially with a velocity of 1.84 m/s, we know that the ball's velocity could not have stayed the same in both magnitude and direction, so the final velocity must be -0.53 m/s.
Now, we can solve for the velocity of the other ball (initial of 0.53 m/s):
vf2 = 1.31 - (-0.53) = 1.84 m/s.
Now, you could have also made the connection that when two balls of the SAME MASS experience an ELASTIC collision, the velocities are simply "exchanged" from one to another. I just used this more "extensive" method to prove this.
