\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}
