In World War I the German army set up an enormous cannon (which they called the "Paris gun") to fire shells at Paris, \(120 \mathrm{~km}\) away from the cannon situated at a point NNE of Paris. The muzzle velocity was \(1640 \mathrm{~m} / \mathrm{s}\).

(a) Neglecting both air resistance and the Coriolis effect, find two solutions for the elevation angle of the gun, assuming the altitudes of the launching and target points were the same.

(b) With these same assumptions, for each of the two possible elevation angles, how long would the shell have taken to reach its target, and what maximum altitude would it have achieved? Compare your results with the actual flight time \(182 \mathrm{~s}\) and maximum altitude \(42 \mathrm{~km}\). What do you think is the primary reason for the large discrepancies?

(c) With the same assumptions as in part (a), calculate the Coriolis deflection of the shell aimed at Paris for the larger elevation-angle solution. Be sure to include the Coriolis deflections due to both the horizontal and vertical components of the shell's velocity. This results might give at least a very rough estimate for the actual Coriolis deflection. For simplicity, assume the shell began traveling due south. Is its deflection toward the east or toward the west?