Question

Sample Question 3. 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 θ=40° and the total velocity V= 140 ft/sec. Determine the value of ?̇ and ?̇. Show the axis r and θ along with velocity (Vθ, Vr, and V) vectors at point P in a diagram.

P 20° 500"

Answer 1

Observe that the direction of r is same as that of rat that instant. Compute the angle blu. sand v. x=0-200 x = 40°-20 = 20° Now compute the magnitude of absolute velocity Losizontal I cos 20° ~= 140 = 148.98f/ Cosao ] It can be interpreted from the diagram that the line os is at angle (900-28+40° fount sox= 110° Compute the range at that particulare instant. za soo Cos(110°- 40°) = 1461.9022 ft consider the expression for angular velocity of the flight with reference to the ponto commsider the expression for absolutely veloury, = ſhe too 149.989= 2 + (1461.9022363 148:992= 1404+( 1461.9022703? Ó = -0.0348 radlsce. "indlates clockwise disection