An airplane with constant airspeed of 525 km/h needs to reach its destination 705 km due north against a steady 95.0 km/h wind blowing from east to west. At what angle with respect to north, should the pilot point the airplane? How long will it take the airplane to reach its destination?

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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An airplane with constant airspeed of 525 km/h needs to reach its destination 705 km due north against a steady 95.0 km/h wind blowing from east to west. At what angle with respect to north, should the pilot point the airplane? How long will it take the airplane to reach its destination?

Expert Solution
Step 1

Consider North direction as positive y axis and East direction as positive x axis.

The velocity of the wind in the vector form can be expressed as,

Mechanical Engineering homework question answer, step 1, image 1

Let us consider that the direction of the velocity of the plane with respect to the y axis (North) is at an angle theta.

Thus, the velocity of the plane in the form of velocity vector can be determined as,

Mechanical Engineering homework question answer, step 1, image 2

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