
\magnification=\magstep2

$$
M v \quad = \quad M v_1 + m v_2
$$

$$
{{1}\over{2}} M v^2 \quad = \quad {{1}\over{2}} M {v_1}^2 + 
                                  {{1}\over{2}} m {v_2}^2
$$


$$
\eqalign{
v_1 \quad &= \quad \left[ 1 - {{2}\over{1 + (M/m)}} \right] v \cr
\cr
v_2 \quad &= \quad \left[ {{2}\over{1 + (m/M)}} \right] v \cr
}
$$

$$
\eqalign{
v_1 \quad &\simeq \quad \left(1 - {{2m}\over{M}} \right) v  \quad \sim \quad v \cr
v_2 \quad &\simeq \quad 2 v \cr
}
$$

\bye
