Answer
a) The ratio is 3.
b) $v_{2f}=2v_{1i}$
Work Step by Step
We know the following equation for elastic collisions:
$v_{1f}=\frac{m_1-m_2}{m_1+m_2}v_{1i}+\frac{2m_2}{m_1+m_2}v_{2i}$
$m_1$ ends up at rest, $v_{1f}$, and $v_{1i}=-v_{2i}$, so it follows:
$\frac{m_1-m_2}{m_1+m_2}=\frac{2m_2}{m_1+m_2}$
$m_1-m_2=2m_2$
$m_1=3m_2$
Thus, the ratio is 3.
b) We use the mass ratio to find the final speed of the second particle:
$v_{2f}=\frac{4m_2}{2m_2}v_{1i}=2v_{1i}$
