Relative velocity of plane with vectors

[Yae Miteo]

Homework Statement

The problem is worded thus:

You are on an airplane traveling 30° south of due west at 130 m/s with respect to the air. The air is moving with a speed 30 m/s with respect to the ground due north.

(a) What is the speed of the plane with respect to the ground?

(b) What is the heading of the plane with respect to the ground? (Let 0° represent due north, 90° represents due east).

Homework Equations

No formulas given

The Attempt at a Solution

I attempted to solve the problem by putting it on a N-E coordinate plane, with two vectors. (North as y, east as x).

For wind:
$$\vec{v} = 0\hat{i} + 30\hat{\jmath}$$
For the plane, I do not know how to set up a vector. My plan was to do so, and then find its magnitude so that I can find the plane's speed relative to the ground. 130 m/s is given as the plane's speed relative to the air, but I need to figure out how to relate that to the ground. Any ideas?

For part b, I think I need to know how to do "a" first.

 

[Student100]

Homework Statement

The problem is worded thus:

You are on an airplane traveling 30° south of due west at 130 m/s with respect to the air. The air is moving with a speed 30 m/s with respect to the ground due north.

(a) What is the speed of the plane with respect to the ground?

(b) What is the heading of the plane with respect to the ground? (Let 0° represent due north, 90° represents due east).

Homework Equations

No formulas given

The Attempt at a Solution

I attempted to solve the problem by putting it on a N-E coordinate plane, with two vectors. (North as y, east as x).

For wind:
$$\vec{v} = 0\hat{i} + 30\hat{\jmath}$$
For the plane, I do not know how to set up a vector. My plan was to do so, and then find its magnitude so that I can find the plane's speed relative to the ground. 130 m/s is given as the plane's speed relative to the air, but I need to figure out how to relate that to the ground. Any ideas?

For part b, I think I need to know how to do "a" first.

Have you tried breaking up the given plane vector into components?

 

[Simon Bridge]

No formulas given

... in the problem statement - but that does not mean there are no relevant equations.

I attempted to solve the problem by putting it on a N-E coordinate plane, with two vectors. (North as y, east as x).

... that's a decent idea.

For wind:
$$\vec{v} = 0\hat{i} + 30\hat{\jmath}$$

Fair enough.

For the plane, I do not know how to set up a vector.

... use trigonometry.

My plan was to do so, and then find its magnitude so that I can find the plane's speed relative to the ground. 130 m/s is given as the plane's speed relative to the air, but I need to figure out how to relate that to the ground. Any ideas?

You could also just use your knowledge of geometry - vectors are arrows pointing in some direction with some length - so sketch them out.
You will need to either add or subtract the vectors to get the result you need.