- #1
Dustinsfl
- 2,281
- 5
We have 2 masses: one with mass \(M\) with velocity \(V_0\) and the other with mass \(m\) and velocity \(0\).
\begin{align}
MV_0 &= MV_0' + mv'\\
M(V_0 - V_0') &= mv'\qquad (*)\\
MV_0^2 &= MV_0^{'2} + mv^{'2}\\
M(V_0 - V_0')(V_0 + V_0') &= mv^{'2}\qquad (**)
\end{align}
So let's take \(\frac{(**)}{(*)}\Rightarrow V_0 + V_0' = v'\)
How do I write \(v'\) and \(V_0'\) in terms of their masses and \(V_0\)?
\begin{align}
MV_0 &= MV_0' + mv'\\
M(V_0 - V_0') &= mv'\qquad (*)\\
MV_0^2 &= MV_0^{'2} + mv^{'2}\\
M(V_0 - V_0')(V_0 + V_0') &= mv^{'2}\qquad (**)
\end{align}
So let's take \(\frac{(**)}{(*)}\Rightarrow V_0 + V_0' = v'\)
How do I write \(v'\) and \(V_0'\) in terms of their masses and \(V_0\)?