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**1. The problem statement, all variables and given/known data**

A 10.0 g marble slides to the left with a velocity of magnitude 0.500 m/s on the frictionless, horizontal surface of an icy, New York sidewalk and has a head-on elastic collision with a larger 30.0 g marble sliding to the right with a velocity of magnitude 0.150 m/s

Find the velocity of each marble (magnitude and direction) after the collision, the change in momentum of each marble, and the change in kinetic energy for each marble.

**2. Relevant equations**

B=bigger marble

S=smaller marble

(mB)(viB) + (mS)(viS) = (mB)(vfB) + (mS)(vfS)

.5(mB)(viB)^2 + .5(mS)(viS)^2 = .5(mB)(vfB)^2 + .5(mS)(vfS)^2

**3. The attempt at a solution**

This problem has been hard for me because I have not figured out how to substitute from one equation to the other. I have solved for the velocity of the Big marble (vfB) but when I substitute it into the kinetic energy equation I end up getting crazy numbers that are hard to simplify.

I solved for vfB and got:

(vfB) = .35(vfS)

When I substitute it though, I get:

.004625 J = .5(.01 kg)*(.05 m/s + 3vfB)^2 + .5(.03 kg)*(vfB)^2

So, I'm getting some pretty crazy numbers that are hard for me to work with. Once I find a final velocity this is going to be easy. Does anyone have a suggestion on how to proceed?