$9\mathrm{.}28**$ Use the result $(9\mathrm{.}73)$ of Problem $9\mathrm{.}26$ to do the following: A naval gun shoots a shell at colatitude $0$ in a direction that is a above the horizontal and due east, with muzzle speed v o$.($a$)$ Ignoring the earth's rotation $($and air resistance$),$ find how long $($t$)$ the shell would be in the air and how far away $($R$)$ it would land. If vo$=500$ m$/$s and a $=20,$ what are t and R$?($b$)$ A naval gunner spots an enemy ship due east at the range R of part $($a$)$ and, forgetting about the Coriolis effect, aims his gun exactly as in part $($a$).$ Find by how far north or south, and in which direction, the shell will miss the target, in terms of Q$,$ v o$,$ a$,0,$ and g$.($It will also miss in the east$$west direction but this is perhaps less critical.$)$ If the incident occurs at latitude $50$ north $(0=40),$ what is this distance? What if the latitude is $50$ south? This problem is a serious issue in long$-$range gunnery: In a battle near the Falkland Islands in World War I, the British navy consistently missed German ships by many tens of yards because they apparently forgot that the Coriolis effect in the southern hemisphere is opposite to that in the north.