Conservation of KE and Momentum?

Question

A 4.00 kg ball (ball 1), moving to the right at a velocity of +3.00 m/s on a frictionless table, collides head-on with a stationary 7.80 kg ball (ball 2). Find the final velocities of the balls if the collision is as specified below.
(a) elastic collision
ball 1
?? m/s
ball 2
?? m/s
(b) completely inelastic collision
ball 1
(I got this right with 1.02 m/s)
ball 2
(I got this right with 1.02 m/s)

I know part one has to do with conservation of KE, but whenever I try to work it, I get a wrong answer. Can someone help me?

Answer 1

Elastic collisions conserver kinetic energy as well as momentum.
So you have two equations in two unknows.

Momentum:
4(3) = 4v1 + 7.8v2

Kinetic Energy

4(3^2) = 4(v1^2) + 7.8(v2^2)

where v1 and v2 are the final velocities of ball1 and ball2.
Now its a math problem - so solve for v1 and v2.

v1 = -.97 m/s
v2 = 2.03 m/s

Answer 2

Jim C gave you the right answer but since you are learning I think it would have been better if he hadn't cut corners in figuring KE.
KE = (1/2)m*V^2
Jim C left out the 1/2 in his equation showing kinetic energy before and after the collision. Didn't matter because each term has the 1/2 and it would cancel out eventually. But better to show that since you're learning.