A plane flies horizontally at an altitude of 2 km and passes directly over a tracking telescope on the ground. When the angle of elevation is 蟺/3, this angle is decreasing at a rate of 蟺/6 rad/min. How fast is the plane traveling at that time?How fast is a plane traveling at a certain time.?Let:
x km be the horizontal distance of the plane from the tracking telescope,
a be the angle of elevation.
x / 2 = cot(a)
dx / dt = - 2 csc^2(a) (da / dt)
Putting a = pi / 3, csc(a) = 2 / sqrt(3), da / dt = - (pi / 6) rad / min:
dx / dt = (- 8 / 3) (- pi / 6)
= (4 pi / 9) km / min.
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