What should its speed be relative to the ground?

[AHuds0n]

Relative Motion - I need help on it and more help

I need help on Relative Motion. I'm about to literally pull my hair out if I don't understand how to do this. I would very appreciate it if someone could help me out with this one problem and I probably could do the other by myself.

The pilot of an aircraft wishes to fly due west in a 50.0 km/h wind blowing toward the south. The speed of the aircraft in the absence of a wind is 205 km/h.

a. In what direction should the aircraft head?
b. What should its speed be relative to the ground?

I've spent at least 3 hours on this homework.

This is what I started out doing:

I sketched a picture of the aircraft's and wind's direction.
The plane was going west 205 km/h and the 50 km/h wind was going south. And I tried finding the displacement using the pythagorean theorem but the answer was wrong. And I divided 205 km/h over 50 km/h and used tan-1 with the anwer to get the direction but it was wrong.

I'm not even sure if I went about the problem right.

 

[quantumdude]

A useful convention to adopt for these relative motion problems would be to call the velocity of the plane with respect to the air v_PA. That is, the first subscript indicates what is moving and the second subscript indicates with respect to what reference frame the body is moving. So, you are given the magnitude of this vector: v_PA=205 km/h. Since you don't know the direction, characterize it by an angle θ and write out the vector in component form.

You are also given the velocity of the air. This should be interpreted as the velocity of the velocity of the air with respect to the ground, and I would call it v_AG. You are further told that the plane is to head due west, which means that the velocity of the plane with respect to the ground is to point in that direction. Call this velocity v_PG.

Why use this notation? Because it makes relative velocity problems a piece of cake. The correct way to write the vector sum is such that the subscripts line up as follows:

v_PG=v_PA+v_AG.

That is, the outer subscripts on the right hand side ("P" and "G") have to match the subscripts on the left hand side, and the inner subscripts in the right hand side ("A" and "A") have to be the same.

Can you take it from there?

 

[AHuds0n]

I think I can.

Thankyou b/c I was so lost.

 

[AHuds0n]

So I add 205 km/h and 50 km/h and get 255 km/h?

And 255 km/h is the Vpg?

What do I do with the Vpg?

I'm more lost than I ever was.

 

[quantumdude]

So I add 205 km/h and 50 km/h and get 255 km/h?

And 255 km/h is the Vpg?

No! These are vectors, so you have to add them as vectors.

Write down a vector to represent each velocity. Write it down in i, j component form.