A plane flies horizontally at an altitude at an altitude of 5 km and passes directly over a tracking telescope on the ground. When the angle of elevation is pi/3, this angle is decreasing at a rate of pi/6 rad/min. How fast is the plane traveling at that time?
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Let x = horizontal distance of the plane from the telescope when the angle of elevation is θ
=> x/5 = cotθ
=> (1/5) dx/dt = - cosec^2 θ * dθ/dt
=> horizontal speed at which the plane is flying is
dx/dt
= - 5cosec^2 θ * (rate of change of angle of elevation)
= - 5 cosec^2 (π/3) * (-π/6)
= (5π/6) * (4/3)
= 10π/9 km/min.
=> x/5 = cotθ
=> (1/5) dx/dt = - cosec^2 θ * dθ/dt
=> horizontal speed at which the plane is flying is
dx/dt
= - 5cosec^2 θ * (rate of change of angle of elevation)
= - 5 cosec^2 (π/3) * (-π/6)
= (5π/6) * (4/3)
= 10π/9 km/min.