How Do You Solve an Elastic Collision Problem with Different Masses?

[harkkam]

Elastic Collision...Problem

The problem states. The collison is elastic and head on. One ball has a mass of m1=.250kg and initial velocity of 5.00m/s. The other has a mass of m2=.800kg and is initially at rest. No external forces act on the ball. What are the velocities after collision.

So far I got up to a certain point and I get stuck.

I deduced that

(Vf1)^2 = (Vo1)^2 - (M2/M1)(Vf2)^2
Vf2 = (M1/M2)(Vo1-Vf1)


Now when I substitute Vf2 into the first equation I get

(Vf1)^2 = (Vo1)^2 - (M2/M1)[(M1/M2)(Vo1-Vf1)]^2

This is where I get stuck. I can't solve for Vf1. I have the answer but I want to learn the steps to get to.

Vf1= (M1-M2/M1+M2)Vo1

Thnks

 

[Doc Al]

Now when I substitute Vf2 into the first equation I get

(Vf1)^2 = (Vo1)^2 - (M2/M1)[(M1/M2)(Vo1-Vf1)]^2

This is where I get stuck. I can't solve for Vf1.

Expand the right hand term, then rearrange so that you end up with a quadratic equation for Vf1.