Question

An airplane flies due west at 120 km/h. At the same time, the wind blows it due north at 40.0 km/h. What is the plane's resultant velocity?
Use Trigonometry on solving the problem.

Answer 1

Here the earth is one reference frame(S) and the air is the other reference frame(S') moving with respect to the first.

Then, u=40 km/h is the velocity of the air with respect to the ground,v'=120 km/h is the velocity of the plane with respect to the air and v is the velocity of the plane with respect to the ground.

The angle a is the angle N of W of the plane's course with respect to the ground and is given by

tan(a)=u/v'=40/120=1/3.

Therefore, a=tan^-1(1/3)=18.4⁰.

The airplane's speed with respect to the ground is given by v=squareroot(v'²+u²)=squareroot(120²+40²)=126.5 km/h.

This is the plane's resultant velocity ie. both its magnitude and the angle it makes with the westward direction.