Problem 6.44

กำหนดให้ \(m_{1} = m, u_{1} = u, m_{5} = 5m\) และ \(u_{5} = 0 m/s\)

จาก \(Σ\vec{p}_{f}= \Sigma \vec{p}_{i}\)

\(m_{1}v_{1} + m_{5}v_{5} = m_{1}u_{1} + m_{5}u_{5}\)

\(mv_{1} + 5mv_{5} = mu + 5m(0)\)

\(v_{1} + 5v_{5} = u\)

\(v_{1} = u - 5v_{5}\)

จาก \(\vec{v}_{1} + \vec{u}_{1} = \vec{v}_{5} + \vec{u}_{5}\)

\(v_{1} + u = v_{5} + 0\)

\(v_{1} + u = v_{5}\)

\((u - 5v_{5}) + u = v_{5}\)

\(v_{5}=\frac{u}{3}\;\blacksquare\)

\(\therefore v_{1} + u = v_{5}\)

\(v_{1} + u =\frac{u}{3}\)

\(v_{1} = -\frac{2u}{3}\;\blacksquare\)