What Is the Velocity of Cyclist B and C Relative to the Road?

[Peter G.]

Hi,

I got the answer to this question wrong; I'll show what I did so you guys can help me spot my misconception:

A cyclist A moves with speed 3.0 m/s to the left (with respect to the road). A second cyclist B, moves on the same straight line path as A with a relative velocity of 1.0 m/s with respect to A.

a) What is the velocity of B with respect to the road?
b)A third cyclist has a relative velocity with respect to A of -2.0 m/s. What is the velocity of C with respect to the road?

My Answers:

a) OK, if the velocity of B relative to A is equal to 1 m/s, they are moving in the same direction, but B is moving faster by 1 m/s, hence, relative to the ground it should be moving at 4 m/s. But the answer is, according to the book, -2 m/s.

b) If C is at -2.0 m/s to A, then it is moving in the same direction as A once again, but, in this case, it must be moving slower because A is seeing it move in the opposite direction, backwards. Since it is at -2,0 m/s in relation to A, it must be at 1 m/s relative to the ground, but the answer according to the book is -5 m/s...

I am lost!

Thanks in advance,
Peter G.

 

[phinds]

If B is going in the opposite direction from A, then he's going -2m/s relative to the ground. Hard to do on a bike but easy in math.

If C is going in the opposite direction from A, then he's going -5m/s relative to the ground.

You need to ask your prof what the hell these guys are doing peddling backwards.

 

[gneill]

It would appear that they want you to set your coordinate system so that velocities to the left are negative. So cyclist A moving with speed 3.0 m/s to the left has a velocity of -3.0 m/s in that coordinate system. Cyclist B, with a relative velocity of 1.0 m/s w.r.t. A (a rightward difference) will still be moving to the left, only a bit slower that A.

In equation form:
Vb - Va = +1.0 m/s
Vb = +1.0 m/s + Va
Vb = +1.0 m/s + (-3.0 m/s) = -2.0 m/s

Similar reasoning should clear up part (b).