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## Homework Statement

"A particle with mass ##m_1=1kg## traveling at ##v_{1_{0}}\frac{m}{s}## collides with a stationary particle with mass ##m_2=2kg##. How small is the speed of ##m_1## after the collision compared to before?"

## Homework Equations

## The Attempt at a Solution

##m_1v_{1_{0}}=m_1v_{1_{f}}+m_2v_{2_{f}}=m_1v_{1_{f}}+2m_1v_{2_{f}}=m_1(v_{1_{f}}+2v_{2_{f}})##

##v_{1_{0}}=v_{1_{f}}+2v_{2_{f}}##

Then this is where I kind of guess at things: basically, I equate the momentum of the first particle post-collision with the momentum of the second particle post-collision.

##m_1v_{1_{f}}-m_2v_{2_{f}}=0##

So now I have two equations:

##v_{1_{f}}-2v_{2_{f}}=0##

##v_{1_{f}}+2v_{2_{f}}=v_{1_{0}}##

Solving for the two variables gives me: ##v_{1_{f}}=\frac{1}{2}v_{1_{0}}## and ##v_{2_{f}}=v_{1_{0}}##. I know this is wrong because suddenly the two particles have more momentum after the collision than what they started out with.