Question

an airplane is flying from montreal to vancouver. the wind is blowing from the west at 60km/h. the airplane flies at an airspeed of 750 km/h and must stay on a heading of 65 degrees west of north. what heading should the pilot take to compensate for the wind? what is the speed of the airplane relative to the ground?

Answer 1

To compensate for the wind, the pilot should take a heading of approximately 16 degrees west of north.

To determine the speed of the airplane relative to the ground, we need to use vector addition. Let's break the airplane's velocity into its components.

The component of the airplane's velocity in the northward direction is given by:

Vn = 750 km/h * sin(65) = 659.67 km/h

The component of the airplane's velocity in the westward direction, taking into account the wind, is given by:

Vw = 60 km/h

Using the Pythagorean theorem, we can find the resultant velocity of the airplane relative to the ground:

Vg = sqrt(Vn^2 + Vw^2) = sqrt((659.67 km/h)^2 + (60 km/h)^2) = 664.43 km/h

Therefore, the speed of the airplane relative to the ground is approximately 664.43 km/h.