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LuckyWell
4 days ago
7

4. An airplane is traveling at a speed of 724 km/hr at a direction of 30 degrees. The wind is blowing from the west at 32 km/hr.

Find the resultant speed and true course of the plane.
Mathematics
1 answer:
lawyer [12.5K]4 days ago
8 0

Answer:

The true course is 28.8 degrees above the east direction.

Step-by-step explanation:

Given:

Direction = 30 degrees

Speed = 724 km/hr

Let x1, y1 represent the velocities in the east direction at a 30-degree angle

therefore, x1 velocity = 724 cos 30 degrees

y1 velocity = 724 sin 30 degrees

According to the problem, the wind speed enhances the x1 velocity by 32.

Thus, the resultant speed becomes

velx1= 659\\vely1 = 362

The \ speed\ is\ determined \ by \ following\ formula\ \\ \sqrt{vel y1^2+ velx1^2} \\= \sqrt{659^2+362^2}\\=751.9 km/hr\\therefore\ \ the\ direction is\ arctan \\= vely1/ velx1 \\= arctan( 362/659) \ =28.8\ degrees\ above\ from\ the\ east

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