Centripetal Acceleration Problem

[sap_54]

Hello,
I am having the worst time figuring out how to solve this problem:

A student build and calibrates an acclerometer, which she uses to determine the speed of her car around a certain unbanked highway curve. The accelerometer is a plumb bob with a prtractor that she attaches to the roof of her car. A friend riding in the car with her observes that the plumb bob hangs at an angle of 15 degrees from the vertical when the car has a speed of 23m/s. What is the centripetal acceleration of the car?

Ok, I have my force equations:

The sum of the forces in the x=-Tcos75=-(mv^2)/r
The sum of the forces in the y=Tsin75-mg=0
I substituted T for mv^2/r, so mass cancels out, but I can't seem to figure out where to go from there.

Any help would be greatly appreciated!

 

[carlz]

I didnt use the speed.

resolve Tcos15 = m 9.81
Tsin15 = ma

divide

9.81tan15 = a

a = 2.628ms^-2