A camera is positioned 250 feet from the base of a misslelaunching pad. If a mis

Question

A camera is positioned 250 feet from the base of a misslelaunching pad. If a missle of length 7 feet is launchedvertically, then the function that relates the angle subtended bythe missle, , to the height, h, is given by (h) =cot-1(250/7+h) - cot-1(250h). Findd/dh. B). If the missle is rising at a rate of 157 ft per second,find the rate at which the subtended angle changes at the momentwhen the missle is 500 feet off the ground? A camera is positioned 250 feet from the base of a misslelaunching pad. If a missle of length 7 feet is launchedvertically, then the function that relates the angle subtended bythe missle, , to the height, h, is given by (h) =cot-1(250/7+h) - cot-1(250h). Findd/dh. B). If the missle is rising at a rate of 157 ft per second,find the rate at which the subtended angle changes at the momentwhen the missle is 500 feet off the ground?

Explanation / Answer

(h) = cot-1[250/(7 + h)] - cot-1(250/h)= tan-1[(7 + h)/250] - tan-1(h/250) A) d/dh = {1 + [(7 + h)/250]2}-1 d[(7 +h)/250]/dh - {1 + (h/250)2}-1d(h/250)/dh = 250-1 * [{1 + [(7 + h)/250]2}-1- {1 + (h/250)2}-1] B) dh/dt = 157 ft/s, h = 500 ft d/dt = d/dh * dh/dt = 157 * 250-1 * [{1 +[(7 + 500)/250]2}-1 - {1 +(500/250)2}-1] = -2.77*10-3rad/s

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