# [SOLVED]Elastic Collision

#### dwsmith

##### Well-known member
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 $$V_0$$?

#### Ackbach

##### Indicium Physicus
Staff member
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 $$V_0$$?
So you could do
\begin{align*}
v'&= \frac{M(V_0-V_0')}{m} \\
V_0+V_0'&= \frac{M(V_0-V_0')}{m}
\end{align*}
Solve for $V_0'$ ...