Instruments located at O are part of the groundtraffic contr

Instruments located at O are part of the ground-traffic control system for a major airport. At a certain instant during the takeoff roll of the aircraft P, the sensors indicate the angle ? = 47° and the range rate r? = 113 ft/sec. Determine the corresponding speed v of the aircraft and the value of ??.

Solution

we know

435^2 =r^2 -s^2

differentiating w.r.t. time,

0= 2 x r x dr/dt- 2x s x ds/dt

as ds/dt=v

so, s x v= r x dr/dt

so, 435x tan 64 x v = 435x sec64 x 113

so, v= 113 x cosec 64= 113 x 1.112= 125.656 ft/s