How Does Wind Affect an Airplane's Flight Path and Speed?

In summary, an airplane flying at 600km/h on a bearing of W38N with a wind of 75km/h from W25S will result in a resultant velocity of 569.877km/h and a direction of N45.26W.
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Homework Statement


An airplane flies at 600km/h on a bearing of W38N while a wind of 75km/h from W25S is present.
Find the planes resultant velocity and direction

The Attempt at a Solution



So here's what I did:

The Airplane: x = 600cos142 = -472.8
y = 600sin142 = 369.39

The Wind: x = 75cos25 = 67.973
y = 75sin25 = 31.69

Sum of x: -472.8 + 67.973 = -404.827
Sum of y: 360.30 + 31.69 = 401.09

Resultant would be using pythagorean theorem:

this gives me 569.877

and the angle would be theta = tan1- (401/-494.877) = -44.734 degreesI think what I did is right (please correct if I am wrong) but I was wondering about my angle. The angle is not below the horizontal right? I just don't understand why its negative. If i were to change it to bearing form would i do... 90-44.734 = 45.26 degrees therefore on a bearing of N45.26W? Please clarify the solution I have found
 
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  • #2
I didn't check your numbers, but the method is correct. The angle is negative because the arctangent returns a value between [itex]-\pi/2[/itex] and [itex]\pi/2[/itex]. You have to look at the signs of x and y to find the actual angle.
 

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