You are traveling on an airplane The velocity of the plane w

You are traveling on an airplane. The velocity of the plane with respect to the air is 100 m/s due east. The velocity of the air with respect to the ground is 37 m/s at an angle of 30degree west of due north. ^1) What is the speed of the plane with respect to the ground? m/S ^2) What is the heading of the plane with respect to the ground? (Let 0degree represent due north, 90degree represents due east). degree East of due North ^3) How far east will the plane travel in 1 hour? m

Solution

v_plane/ground = v_plane/air + v_air/ground

v_x = 100 - 37 * sin 30 = 81.5

v_y = 37 * cos 30 = 32.04

magnitude = sqrt [81.5² + 32.04²]

= 87.57 m/s

-------------------------------------------------

theta = tan-1 [32.04 / 81.5]

= 21.45 deg

-------------------------------------------------

x = v_x * t = 81.5 * 60 * 60

= 293400