Finding the speed of car A and car B

[meeklobraca]

Homework Statement

At the instant shown, race car A is passing race car B with a relative velocity of 1ft/s. Knowing that the speed of both cars are constant and that the relative acceleration of car A with respect to Car B is 0.9ft/s^2 directed toward the center of curvature, determine the speeds of cars A and B.

The diagram is located here: Problem 134

http://www.smccd.net/accounts/enriquez/Engr240Files/Problemset3.pdf

Thank you!

Homework Equations

The Attempt at a Solution

With the relative acceleration being what it is in the j direction, I plugged in 0.9 = vb^2/p - va^2/p and plugged in a 3+Va for vb. That doesn't work. What should I do here?

Thanks!

 

[rl.bhat]

Acceleration of the car in a circular motion is
a = v^2/r. Or
a*r = V^2.
So for larger radius acceleration is smaller. For car A
a*r(a) = V^2...(1)
For car B
(a - 0.9)r(b) =(V+3)^2...(2)
Solve the two equations.

 

[meeklobraca]

doing that I get an unsolvable quadratic...

 

[rl.bhat]

The two cars are moving together with constant velocity. So they must have the same angular velocity.
The acceleration a = ω^2*r.
So (a + 0.9) = ω^2*300
and a = ω^2*290. Now solve for a.
Then use a = V^2/r to find velocities of the cars.