## Essential University Physics: Volume 1 (4th Edition)

a) The ratio is 3. b) $v_{2f}=2v_{1i}$
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: $v_{2f}=\frac{4m_2}{2m_2}v_{1i}=2v_{1i}$