How would you find the components of the velocity vector in the northerly and westerly directions?

Question

The airplane is traveling 900km/h in a direction 38.5 degree west of north.
The answer is north is 704 km/h and west is 560 km/h.
Please can u show me how to solve for it

Answer 1

So imagine a cartesian coordinate system where +z is north -z south, -x west, +x east.

38.5 deg west of north means that the angle between the velocity and the +z axis is 38.5 degrees.

We simply use the sin and cos functions to find this.

We know that

sin(deg) = opposite/hypoteneuse

We will use sin to find the westernly direction and cos to find the northernly direction due to the fact that 38.5 deg is measured from the z axis.

Thus

900*sin(38.5) = 560
900*cos(38.5) = 704

Answer 2

You would use trig to solve this problem:sin(38.5)*900=560 and cos(38.5)*900=704.