In 1914 there was a World War I naval battle between British and German battle cruisers near the Falkland Islands, at \(52^{\circ}\) south latitude (i. e., \(\lambda=-52^{\circ}\).) Guns on the British ships fired 12-inch shells at German ships up to about \(15 \mathrm{~km}\) distant. The great majority of the shells missed their targets, due to the constant rolling of the ships, defensive maneuvers by the Germans, and perhaps other factors. After the battle (which the British won) another possible reason was offered: Coriolis deflections. The story goes that the British were used to battles in the northern hemisphere, where projectiles deflect toward the right, and aimed their guns incorrectly for the Falklands battle, where projectiles deflect toward the left. There seems to be some controversy over whether or not Coriolis effects were important in the battle. The purpose of this problem is to estimate their magnitude.

The British guns reportedly had a muzzle velocity of \(823 \mathrm{~m} / \mathrm{s}\).

(a) For a target \(15 \mathrm{~km}\) away, and pretending there was no air resistance, what must have been the elevation angle (the angle up from the horizontal) of the guns? Note that the guns were apparently limited to elevation angles of \(15^{\circ}\) or less.)

(b) By about how much would the shells have missed their target due to the sideways Coriolis effect? (Note that if the British used gun-aiming tables appropriate for \(52^{\circ}\) north latitude, which is appropriate for the north Atlantic, then the miss distance of the shells would have been about twice as much as the southern hemisphere deflection alone.)