Deriving Final Equation from Equations 1 & 2

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To derive the final equation from Equations 1 and 2, start by rearranging Equation 2 to express m1. Substitute this expression into Equation 1 and simplify. This process leads to a form that includes terms like v1f(v2f^2 - v2i^2) and v2i(v1i^2 - v1f^2). Recognize that the difference of squares, (v2f^2 - v2i^2), can be factored into (v2f - v2i)(v2f + v2i) for further simplification. Following these steps will help achieve the final equation successfully.
caligyrl4lyfe
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HI I need help with the steps in between? I am totally confused...

So, how to derive the final equation from equation 1 and 2


m1v1i+m2v2i=m1v1+m2v2f (Equation 1)

1/2m1V1i^2+1/2m2v2i^2=1/2m1v1f^2+1/2m2v2f^2 (Equation 2)

v1i-v2i= -(V1f-v2f) ( Final Equation)
 
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ok it does work out just abit of algebra

First off what i did was rearrange your 2nd equation in terms of m1

Substitute m1 into your first equation and simplify down

you will end up with something like v1f(v2f^2-v2i^2)+v2i(v1i^2-v1f^2)=something

now you have to realize that (v2f^2 - v2i^2) = (v2f - v2i)(v2f + v2i)

More simplification from there and than you are done

(Tip don't expand all the brackets out it will drive you nuts, rather cancel them down after recognizing that "now you have to realize that (v2f^2 - v2i^2) = (v2f - v2i)(v2f + v2i)"

Thus from that you should get what are looking for

Cheers Trent
 
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