A tracking radar is locked on an airplane flying at a constant altitude of 5km,

Question

A tracking radar is locked on an airplane flying at a constant altitude of 5km, and a constant speed of 540 km/h. The airplane travels along a path that passes exactly above the radar. The radar starts the tracking when the airplane is 100km away. Derive an expressions for the angle theta of the radar antenna as a function of time. Derive an expression for the angular velocity of the antenna, dtheta/dt, as a function of time. Make two plots on the same page, one of theta vs. time and the other of dtheta/dt vs. time, where the angle is in degree s and the time is in minutes for 0 t 20 min.

Explanation / Answer

taking the derivitive of (t) will give us the angularvelocity function (t) d/dt arccot (u) = -du/(1+u^2) u= 20-108*t du=-108 (t)= 108 / ( 1+ (20-108*t)^2)

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