You are standing on the ground at the origin of a coordinate system. An airplane

Question

You are standing on the ground at the origin of a coordinate system. An airplane flies over you with constant velocity parallel to the x axis and at a constant height of 7.05 103 m. At t = 0, the airplane is directly above you so that the vector leading from you to it is 0 = 7.05 103 m. At t = 30.0 s the position vector leading from you to the airplane is 30 = (7.18 103 + 7.05 103) m as suggested in the figure below. Determine the magnitude and orientation of the airplane's position vector at t = 55.0 s. magnitude m direction

Explanation / Answer

v = 7.18e3/30 = 239.333 m/s

x55 = 239.333 * 55 = 13163.315 m

magnitude = (13163.315*13163.315+7.05e3*7.05e3) = 14.9e3 m

direction Arctan(7.05e3/13163.315) = 28.2° above the horizontal.

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