(Solved): A bullet of mass m is fired horizontally with a speed vO toward a hanging block of mass M, as sh ...

A bullet of mass $m$ is fired horizontally with a speed $v_{\mathrm{O}}$ toward a hanging block of mass $M$, as shown below. The bullet lodges itself into the block, and the two have a speed $v$ immediately after the collision. The block-with-bullet then swings upward, reaching a maximum vertical displacement $h$ above its starting height. (a) Represent $v$ in terms of $m,v_{\mathrm{O}}$ and $M$. [4 pts] (b) Represent $h$ in terms of $m,v,M$ and $g$. [4 pts] (c) Represent the increase in the internal energy of the bullet-block system in terms of $m,v_{\mathrm{O}},M,g$, and $h$. [2 pts]