Conservation of energy and fricion

[haha01hah]

Homework Statement

Got an assignment from the teacher to present a problem I have made by myself and show how I have done it, so I have no answer to refer to in this particular question. Anyways,

A car is pushed so that it gains a speed of 2m/s just off a steep road, which has an angle of 35 degrees from the ground. Assume the friction constant is 0.07 from the top to the bottom of the hill. After the steep road, the road is straight. Between the tires and the ground on this straight road the friction is 0.08. The difference in height is 133 meters (from the straight ground to the top of the hill). Assume no force other than the friction that is working against the motion. I want to calculate the distance before it stops.

So I have calculated the speed at the bottom, which is 49,3 m/s. But, to calculate the distance the car needs to stop I use;

$$1/2mv^2+mhg=1/2mv_0^2+mgh_0+W_R$$

Ok, now to my question;
I know that I should cancel out the first two terms (1/2 mv^2 + mgh), but am I allowed to calcel out $$mgh_0$$ because I don't anymore do use the height difference, given that I already calculated the speed at the beginning of the straight road?

Homework Equations

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The Attempt at a Solution

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[PhanthomJay]

Sure. If you started at the top of the hill as your initial point, and used the end of the motion as your final point, then you'd have to include the initial PE. But since you did it the other way, you can omit the PE terms on both sides.