\begin{problem*}{9.56}
Figure P9.56 shows three points in the operation of the ballistic
pendulum discussed in Example 9.6 (and shown in Fig.~9.9b).  The
projectile approaches the pendulum in Figure P9.56a.  Figure P9.56b
shows the situation just after the projectile is captured in the
pendulum.  In Figure P9.56c, the pendulum arm has swung upward and
come to rest at a height $h$ above its initial position.  \Part{a}
Prove that the ratio of kinetic energy of the projectile-pendulum
system immediately after the collision to the kenetic energy
immediately before is $m_1/(m_1+m_2)$.  \Part{b} What is the ratio of
the momentum of the system immediately after the collision to the
momentum immediately before?  \Part{c} A student believes that such a
large decrease in mechanical energy must be accompanied by at least a
small decrease in momentum.  How would you convince this student of
the truth?
\end{problem*}

\begin{solution}
\end{solution}
