An airplane whose airspeed is 580 km/h is supposed to fly a straight line 38 degrees north of east. a steady 82 km/h wind is blowing from the north. in what direction should the plane head?

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facundo3141592 facundo3141592 · Answer 1 · 2022-02-01T14:19:45+01:00

We will see that the plane must travel at 44° north of east.

If the airplane travels with an angle θ measured north from east, the components of the velocity will be:

If we also add the wind, that flows from north, the components of the plane's velocity will be:

Now we want our plane to travel 38° north of east, if you see this like a right triangle, then we must have:

Tan(38°) = (north component)/(east component)

0.78 = tan(θ) - (82/580)*(1/cos(θ))

0.78 = tan(θ) - (0.14/cos(θ))

This must be solved graphically, and the graph of the equation is shown below, there, you can see that the first root is x = 0.773

This is in radians, remember that:

3.14 rad = 180°

Then:

0.773 rad = (0.773/3.14)*180° = 44°

This means that the plane must fly at 44° north of east.

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