A bomber plane, about to drop a bomb, suffers a malfunction of its targeting computer. The pilot notes that there is a strong horizontal wind, so she decides to release the bomb anyway, directly over the visually sighted target, as the plane flies over it directly into the wind. She calculates the required ground, speed, of the aircraft for her flying altitude of 50,000 feet and realizes that there is no problem flying her craft at that speed. She is perfectly confident that the wind speed wall offset the plane’s speed and blow the bomb “backwards” onto the intended target. She adjusts the ground speed of the aircraft accordingly and informs the bombardier to release the bomb at the precise instant that the target appears directly below the plane in the crosshairs of his visual targeting device. Assume that the wind is blowing horizontally throughout the entire space below the plane with a speed of 60 mph, and that the air density docs not vary with altitude. The bomb has a mass of 100 kg. Assume that it is spherical in shape with a radius of 0.2 m.
(a) Calculate the required ground, speed of the plane if the bomb is to strike the target.
(b) Plot the trajectory of the bomb. Explain why the “trailing side” of the trajectory is linear.
(c) How precisely must the pilot control the speed of the plane if the bomb is to strike within 100 m of the target?
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