A plane takes off from an airport with velocity vector (50, 100, 4). Assume that the units are miles per hour, that the positive x-axis points east, and that the positive y-axis points north. (a) How fast is the plane climbing vertically at takeoff? (b) Suppose the airport is located at the origin and a skyscraper is located 5 miles east and 10 miles north of the airport. The skyscraper is 1,250 feet tall. When will the plane be directly over the building? (c) When the plane is over the building, how much vertical clearance is there?
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