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 190 m/s due east. The velocity of the air with respect to the ground is 35 m/s at an angle of 30° west of due north.

1)What is the speed of the plane with respect to the ground?

2)What is the heading of the plane with respect to the ground? (Let 0° represent due north, 90° represents due east).   ° East of due North

3)How far east will the plane travel in 1 hour?

Solution

v_y = 35 * cos 30 = 30.31 m/s

v_x = 190 - 35 sin 30 = 172.5 m/s

magnitude = sqrt [30.31² + 172.5²]

= 175.14 m/s

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direction = tan-1 [30.31 / 172.5]

= 9.98 deg

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x = v_x t = 172.5 * 60 * 60

= 621000 m = 6.21 * 10⁵ m