AP calculus AB

A spy tracks a rocket through a telescope to determine its velocity. The rocket is traveling vertically from a launching pad located 10 km away. At a certain moment, the spy's instruments show that the angle between the telescope and the ground is equal to pi/3 and is changing at a rate of 0.5 radians/min. What is the rocket's velocity at that moment?

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  1. tan T = h/10
    h = 10 tan T
    dh/dt = 10 d(tan T)/ dt = 10 (sec^2 T) dT/dt
    dh/dt = 10 (1/cos^2 pi/3) (.5)
    cos pi/3 = cos 60 = sin 30 = 1/2
    dh/dt = 10(4)(.5) = 20 km/min = 20,000 m/min
    = 20,000 m/min *1 min/60s = 333 m/s

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  2. See, they are all the same.

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  3. I'am very happy so much thank's

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