(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

ok so I was trying to figure out how to derive the formula for true elastic collision and I came up with the following but I want to make sure I didn't make a mistake.

2. Relevant equations

(K1+K2)before=(K1+K2)after

1/2 m_{1}v_{1}^2 + 1/2 m_{2}u_{1}^2 = 1/2 m_{1}v_{2}^2 + 1/2 m_{2}u^{2}^2

m_{1}v_{1}+ m_{2}u_{1}=m_{1}v_{2}+ m_{2}u_{2}

3. The attempt at a solution

(1/2 m_{1}v_{1}^2 + 1/2 m_{2}u_{1}^2 = 1/2 m_{1}v_{2}^2 + 1/2 m_{2}u^{2}^2)*2

m_{1}v_{1}^2+m_{2}u_{1}^2=m_{1}v_{2}^2+m_{2}u_{2}^2

m_{1}(v_{1}^2-v_{2}^2)=m_{2}(u_{2}^2-u_{1}^2) *(1)

m_{1}v_{1}+m_{2}u_{1}=m_{1}v_{2}+ m_{2}u_{2}

m_{1}(v_{1}-v_{2})=m_{2}(u_{2}-u_{1}) *(2)

(1)/(2)

=

v_{1}+v_{2}=u_{1}+u_{2}

u_{2}=v_{1}+v_{2}-u_{1}

m_{1}v_{1}+ m_{2}u_{1}=m_{1}v_{2}+ m_{2}(v_{1}+v_{2}-u_{1})

m_{1}v_{1}+ m_{2}u_{1}=m_{1}v_{2}+ m_{2}v_{1}+m_{2}v_{2}- m_{2}u_{1}

2m_{2}u_{1}+m_{1}v_{1}-m_{2}v_{1}=v_{2}(m_{1}+m_{2})

v_{2}= (2m_{2}u_{1}+v_{1}(m_{1}-m_{2})) / (m_{1}+m_{2})

EDIT: the point of this is that my friend told me that the derivation will take more than 3 pages so I am thinking there must be something incorrect here or I ate some lines lol.

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# Homework Help: Fully perfect elastic collision

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