How do I calculate the necessary speed and direction for a plane to offset wind?

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To calculate the necessary speed and direction for a plane to offset wind, the pilot must account for the wind blowing from the west at 60 km/hr while aiming to fly at 600 km/hr on a bearing of 240 degrees. Bearings are measured clockwise from north, which is crucial for accurate calculations. The pilot can use relative velocity formulas and trigonometric functions to determine the adjustments needed for speed and angle. Initial calculations suggest a resultant speed of approximately 652.64 km/hr with an angle of 30 degrees, but further adjustments may be needed for accuracy. The discussion emphasizes the importance of correctly applying the Pythagorean theorem and trigonometric functions in these calculations.
Charles C
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I know that this should be simple, but I really can't find out how to do this:
A pilot needs to fly at 600km/hr on a bearing of 240 degrees to be on time and on course. A wind is blowing from the west at 60km/hr. In what direction and at what speed should she fly her plane to offset the effect of the wind?

One question I have is when it says "on a bearing of 240 degrees", do you count clockwise or counterclockwise?

I will greatly appreciate any help.

Eh, I think I posted in the wrong area, feel free to to move this.
 
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Bearings are generally given as the angle that is measured clockwise from north. Now you can use the formula for relative velocity.
 
Could you explain the diagram?
 
the speed of the plane is 600, so 600sin30 is 300 and 600cos30 is 519.6. The wind coming from the west is 60, so to compensate for that, I add the 60 to the 300 and get 360. Then I use the Pythagorean theorem to get 632.
Actually, I think I may have done it wrong cause I'm pretty sure I'm supposed to get a different angle.
 
You have to compenste by adding 60 to 600*cos 30. Then you'll get the correct answer.
 
Shooting star said:
You have to compenste by adding 60 to 600*cos 30. Then you'll get the correct answer.
So it would be 652.64 with theta=30?
 
I'm leaving that to you. You know how to multiply. I have to do something now.
 
Quite correct. Now find the angle in which the plane has to go.
 

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