# Using the Elastic equation to find the final velocity

#### MyMotto

1. Homework Statement

A ball of mass 0.440 kg moving east (+x direction) with a speed of 3.30 m/s collides head on with a .220 kg ball at rest. If the collision is perfectly elastic what will be the speed and direction of each ball after the collision?

2. Homework Equations

(.5)m1v1+(.5)m2v2=(.5)m1v1'+(.5)m2v2'

v1= m1-m2/m1+m2(v1) <---I want to how they got from the elastic equation to this

3. The Attempt at a Solution

Really more than anything I want to figure out how to derive the equation to find velocity. I've looked it up and I don't understand all the steps it took. So far I've figured out that
(.5)m2v2 is equal to zero. So the equation is (.5)m1v1= (.5)m1v1'+(.5)m2v2'. I want to understand every part before I start trying to find the solution.

I don't really understand physics so please be very specific. :/

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#### lightgrav

Homework Helper
v2 = 0 only if the balls have the same mass.
"elastic" means that their relative speed (outward) after the collision
is 1x their relative speed (inward) before the collision ... they bounce.

so elastic means that v1 - v2 = v2' - v1'

The formula you showed mixes object properties ... notice m2/m1, and m2(v1)
so was derived for some special case (perhaps not _your_ special case)
... avoid these special-case formulas if you want to understand.

("totally inelastic" means that their relative speed (outward) after the collision
is 0x their relative speed (inward) before the collision ... they stick.)

your first equation would be "momentum conservation", very important
... if you drop all the ½ factors.

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