1. ## Vector problem

A plane is headed due west with an air speed of 212 km/hr. It is driven from its course by a wind from due north blowing at 23.6 km/hr. Find the ground speed of the plane and the actual direction of travel.

I'm not sure how to complete this problem correctly. Here is what I have so far:
Vw=-23.6j Vp=-212i
Vtotal=-212i+-23.6j
tan(theta)=23.6/212 --> theta=6.35 degrees

The plane is heading West of South at 6.35 degree. But How do I calculate the ground speed of the plane? Please help!

2. ## Re: Vector problem

It always can be useful to make a design. Have you done that? ...

3. ## Re: Vector problem

Design is provided in the problem

4. ## Re: Vector problem

Originally Posted by metelskiy
Design is provided in the problem
Draw a right triangle in standard position with terminal side in the third quadrant.
The "opposite" side is 23.6
The hypotenuse is found using the Pythagorean Theorem.
So you're 1 step away.

5. ## Re: Vector problem

Originally Posted by TheChaz
Draw a right triangle in standard position with terminal side in the third quadrant.
The "opposite" side is 23.6
The hypotenuse is found using the Pythagorean Theorem.
So you're 1 step away.
Ok I found the speed to be 213.31km/hr. So will my final answer be correct if I say that the plane is traveling at speed of 213.31km/hr west of south at 6.35 degrees?

6. ## Re: Vector problem

Originally Posted by metelskiy
Ok I found the speed to be 213.31km/hr. So will my final answer be correct if I say that the plane is traveling at speed of 213.31km/hr west of south at 6.35 degrees?
All your calculations are OK. But..

The plane is travelling 6.35° south of west. Better use the course over ground (COG) which is 263.65°.