Question

A very heavy object moving with velocity v collides head-on with a very light object moving with velocity -v. The collision is elastic, and there is no friction. The heavy object barely slows down. What is the speed of the light object after collision?

Answer 1

\[v_1 = \frac {m_1 - m_2}{m_1 + m_2} u_1 + \frac{2m_2}{m_1 + m_2} u_2\]
since \(m_1<<m_2\), and \(u_1= -v, u_2=v\)
\[v_1 = \frac {- m_2}{ m_2} -v + \frac{2m_2}{ m_2} v\]
\[v_1 = v + 2 v\]
\[v_1 =3v\]