##### 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.

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).

3)

How far east will the plane travel in 1 hour?

Thank you for the opportunity to help you with your question!

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.

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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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