# A ball with a mass of #1 kg # and velocity of #7 m/s# collides with a second ball with a mass of #6 kg# and velocity of #- 4 m/s#. If #40%# of the kinetic energy is lost, what are the final velocities of the balls?

##### 1 Answer

#### Explanation:

KE initial=

KE initial=

KE initial= 72.5 J

If 60% KE is conserved then 72.5*.6= 43.5 J is KE final

Another consideration: momentum, p, must be conserved.

Momentum before = momentum after

Solving for

Going back to the kinetic energy

Plugging in the expression for

Now I will multiply thru by 2, multiply thru the first set of parentheses by that 1 kg, and substitute

Now, notice the units in that equation. It is clear that all terms are energy and that

My working of the quadratic equation yields 2 values and neither is obviously invalid.

#v_1 = -4.62 m/s, -0.24 m/s#

Let's see what value for

Repeating with the other result from the quadratic equation work,

I expected a clear-cut way to eliminate one of those results. I do notice that both balls are going the direction that the second ball was going before the collision. Therefore the solution that has

I will post this now but review my work and ask for a double check.

I hope this helps,

Steve