Final answer:
The velocity of cyclist A with respect to cyclist B is 2r(π - 1)/T.
Step-by-step explanation:
When cyclist A travels along the circular track, their velocity with respect to cyclist B can be determined by considering their motion relative to each other.
As cyclist A travels in a circular path, they experience centripetal acceleration directed towards the center of the circle.
This centripetal acceleration causes a change in velocity for cyclist A with respect to B.
To calculate the velocity of A with respect to B, we can use the formula:
vA/B = vA - vB
Where vA/B is the velocity of A with respect to B, vA is the velocity of cyclist A along the circular track, and vB is the velocity of cyclist B along the diameter of the circle.
Since cyclist A travels along a circular track, their velocity can be represented by the formula:
vA = 2πr/T
Where r is the radius of the circular track and T is the time it takes for cyclist A to complete one full revolution.
Cyclist B travels along the diameter of the circle, so their velocity can be represented by:
vB = 2r/T
By substituting these equations into the first formula, we can find the velocity of cyclist A with respect to B:
vA/B = 2πr/T - 2r/T
Simplifying this equation gives us:
vA/B = (2πr - 2r)/T
This can be further simplified to:
vA/B = 2r(π - 1)/T
So the velocity of cyclist A with respect to B is 2r(π - 1)/T.