Relative Velocity of Object C to Object A = 10 m/s

[nguyensteve]

Homework Statement

If the relative velocity of object B to object A is 10 m/s, and the relative velocity of object C to object B is 10 m/s, what is the relative velocity of object C to object A?

Homework Equations

These should be vectors just to give a heads up

v_bs= v_bw+v_ws

v_ba=v_ab

These are the equations given in my book

The Attempt at a Solution

My first attempt was using the second eqaution since the question before it was similar but it did not have c and I used the second formula and I got it right.
The second formula uses the idea of reference frames. So A and B have the same magnitude but different direction. So B and C is the same. So -10m/s -10m/s= -20 m/s. I was given this option and was told it was wrong. Then I made it an absolute value and it was wrong. So would it be -10m/s + 10m/s. Because if B is -10m/s, the opposite magnitude would be 10m/s and adding them together would give me 10? Or would I need more information to solve this.

 

[Daniel Dey]

Convert B wrt A to A wrt B giving -10 then make point diagram of A B and C showing C 10 B 0 and A -10 meter per second this will give you the answer. Hope this helps.

 

[nguyensteve]

So was I on the right track making one of them -10m/s and the other one 10m/s. So at this point do I add them to find the relative velocity of C to A. Making it 0 m/s? I find this part really confusing

 

[Daniel Dey]

No no you are not adding scalars, you are adding vectors afyer this step you have to go to A frame getting B = 10 and C = 20

 

[Daniel Dey]

For relative velocity wrt to A you always have to be in A's frame or can you use common sence. Always remember this point. Good question.

Cheers

 

[nguyensteve]

I still don't understand this. I find it hard to visualize.

 

[Daniel Dey]

Then you need an offline physical world teacher to help you.

 

[haruspex]

v_ba=v_ab

Do you mean v_ba=-v_ab?

Convert B wrt A to A wrt B

Why do that? The first equation applies immediately.

 

[Daniel Dey]

Just ro help you visualise

 

[Daniel Dey]

Do you mean v_ba=-v_ab?

Why do that? The first equation applies immediately.

Yes