How to Determine Relative Velocity Using Vector Subtraction

[Peter G.]

Two objects X and Y are moving away from Point P. The diagram I linked shows it.

It then asks us: Which of the following velocity vectors represent the velocity of X relative to Y.

The answer is B, but the same book told me in another part that we should subtract vectors to get the relative velocity, so: Vector X, east, + (-vector north) = east + south vectors, which would give me Answer A. I am confused, can anyone help me?

Thanks in advance,
Peter G.

 

[SammyS]

What is the velocity of P relative to Y?

 

[Peter G.]

- Velocity Y?

 

[SammyS]

- Velocity Y?

So, you have the velocity of P relative to Y, and the velocity of X relative to P. That should lead you to the velocity of X relative to Y. Hmm ... that does look like V_X + -V_Y

Alternatively: What is the displacement of X relative to Y ?

Added in Edit: Oh! I see. You're right, the answer is A, not B. (That's the answer I was getting all along. I have no Idea how they got B !)

 

[Peter G.]

Yeah, I might have copied the answer from the board incorrectly, because when I drew it, I always got this: (Attachment called Answer)

And, if you don't mind, just another quick doubt: An observer sees a bird flying at 10 m/s east. A second observer, driving a car along the road at 20 m/s in a north direction sees the bird. What is the velocity of the bird relative to the driver?

I get the magnitude correct, but they answer the direction as an angle of 26.5 degrees, and I am unsure of what angle that actually is, can you check to see if it is the one I'm showing in my diagram? I thought they would give the answer as a bearing, since, so far, this it was conventional as an answer for me, but I might have done it wrong.

Thanks once again

 

[Mr.A.Gibson]

You are correct with the angle.
Tan O = opp／adj
O = Inv tan 10/20
O = 26.6

Sorry for the poor lettering hope this makes sense.