Question

a plane is going East at a speed relative to the air of 160 m/s. a 30.0 m/s wind is blowing toward the south while the plane is traveling. The velocity of the plane to a ground observer is:

Answer 1

In order to find the velocity of the plane v relative to the observer we shall be using the velocity addition theorm as follows

Here, V_P and v _w represent the plane and the air speeds, respectively.

Now plane is in East and air is along south so both are perpendicular to each other. Assuming that the east is in positive x-direction and then South will be along -y-direction so the above equation becomes

The magnitude of v can be obtained as

The angle for finding the direction theta can be obtained as

The negative sign shows that the plane will move along south through an angle of 10.62 degree. As the plane has bend a little towards the wind direction so it is getting a little acceleration by the wind so its resultant speed looks like 162.78 m/s