- #1

testme

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## Homework Statement

Two billiard balls of equal mass undergo a perfectly elastic head on collision. If one ball's initial speed was 2.00 m/s, and the other's was 3.00 m/s in the opposite direction, what will their speeds be after the collision?

Va = 2 m/s

Vb = 3 m/s

## Homework Equations

MaVa + MbVb = MaVa' + MbVb'

1/2MaVa^2 + 1/2MbVb^2 = 1/2MaVa'^2 + 1/2MbVb'^2

## The Attempt at a Solution

Let right be positive.

MaVa + MbVb = MaVa' + MbVb'

Va + Vb = Va' + Vb'

2 - 3 = Va' + Vb'

Va' = -1 - Vb'

1/2MaVa^2 + 1/2MbVb^2 = 1/2MaVa'^2 + 1/2MbVb'^2

Va^2 + Vb^2 = Va'^2 + Vb'^2

4 + 9 = (1-Vb')^2 + Vb'^2

0 = -13 + 1 + 2Vb' + Vb'^2 + Vb'^2

0 = 2Vb'^2 + 2Vb' - 12

0 = Vb'^2 + Vb' - 6

0 = (Vb' + 3)(Vb' - 2)

Vb' = -3 or Vb' = 2

I can figure this out, but I'm not sure which answer to choose and also for future questions how I know which to choose.

If Vb' = -3:

Va' = -1 - Vb'

Va' = -1 - (-3)

Va' = 2

If Vb' = 2:

Va' = -1 - Vb'

Va' = -1 - 2

Va' = -3