Work and kinetic energy problem

[rwinge]

Homework Statement

A roller coaster car with a mass of 2000 kg is initially moving at 10 m/s (when it is at the bottom of the "loop-the-loop" portion of the roller coaster track). The loop has a diameter of 16 meters.

The combined effect of air resistance and friction is to produce an average force of 1500 N on the roller coaster car.

How far will the car have moved vertically when its speed has been reduced to 5 m/s?

Homework Equations

K= 1/2(mv^2)f - 1/2(mv^2)i
s=r(theta)
r/(3.14/2) = [r-(delta y)/((3.14/2)-theta)]

The Attempt at a Solution

I was able to find the change in kinetic energy to be 75,000 J.
If I could draw a picture in here I would but I have made a triangle and used the bottom equation above to set up solving for the angle that the rollercoaster would reach at its peak vertical height. However I can't come up with a formula that will hold true for all angles. Does anyone have any ideas as where to move further

 

[AvroArrow]

? I used the equation K= 1/2(mv^2)f - 1/2(mv^2)i to solve for the final velocity (5 m/s). I then tried to use the equation s=r(theta) to solve for the theta, and then the equation r/(3.14/2) = [r-(delta y)/((3.14/2)-theta)] to solve for the delta y (distance moved vertically). However, I can't come up with a formula that will hold true for all angles. Does anyone have any ideas as where to move further?