Question

A pilot wants to fly a plane due north. The speed of the plane relative to the air is 293 km/h and the wind is blowing from west to east at 117 km/h. Calculate the direction (the angle in degrees relative to the north direction) should the plane head? (Your result must contain 1 digits after the decimal and 2% of error will be tolerated in your answers.)

Answer 1

Let the man flow the plane at an angle of alpha from the north towards the West direction.

Now V(plane wrt to wind) + V wind = Vactual velocity of plane.

-293 sin(theta) i + 293 cos(theta) j + 117 i = Vactual velocity

Now the actual velocity should only have a j component and the I component should cancel out each other,

117 = 293 sin(theta)

sin(theta) = 0.4

theta = 23.58 °

So the plane should head at an angle of 23.58° west of North.