Relative and circular motion

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Relative and circle motion

You are traveling on an airplane. The velocity of the plane with respect to the air is 160 m/s due east. The velocity of the air with respect to the ground is 41 m/s at an angle of 30° west of due north.

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

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

How far east will the plane travel in 1 hour?

Sep 2nd, 2015

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The air is moving with a speed 41 m/s an angle of 30° west of due north. Airplane is moving with a speed 160 m/s with respect to air due east.

(a) speed of Airplane with respect to the ground :

Since the wind is having a speed of 41 m/s , it will move the air plane toward North as far as the earth is concerned . Hence we add the speed with the plane’s speed and find the resultant of these two speeds.
Since they are perpendicular to each other, the resultant is

√ (160 ^2 + 41^2) = 165.169 m/s and the direction is given by tan θ = northern  velocity / Eastern velocity so that θ is the angle measured from North to west.
tan θ = 41 / 160 and θ = 14.373° east of north .

hence the speed of airplane is 165.17 m/s at angle 14.373° east of north viewed from the ground.
The speed of the plane in the west direction is 165.17 cos 14.373° = 160.20 m/s
 we know  the speed of the air plane with respect to the ground , and with respect to air will be the same since the wind is flowing perpendicular the planes’ speed .

hence Distance traveled  in one hour = 160.20* 3600 =576708.7 m or 576.71km

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