First! Let me state! I know the answer to this question! It is 400! I say this w

Question

First! Let me state! I know the answer to this question! It is 400!

I say this with exclamation because I will not award karma to someone who posts just the answer to this question.

I will be tested on this concept, and I need a clear outline to help me understand how to solve the problem, and NOT just the answer.

The first person who can clearly post an outline of how to solve this problem, and provide a step by step systematic approach to the problem will be awarded karma. If any steps or equations are not clearly stated before calculating, I will not award karma.

Here is the problem:
A car traveling at 26m/s runs out of gas while traveling up a 5.0 degree slope. How far will it coast before starting to roll back down?

Explanation / Answer

Let us call the point at which the car runs out of gas to be zero.

At point zero the car will have only KE

KE = .5mv2

It will move up the slope and gain PE. Since the law of conservation of energy says that the PE gained must be the KE lost. we can say...

PE = mgh

PE = KE

mgh = .5mv2    (Note m cancels)

Solve for h

h = (.5)(v2)/g

h = (.5)(26)2/9.8

h = 34.5 m

That is the height, but it is rolling along an incline, and we are asked basically how far along the incline the car will roll. The height is the opposite side of a right triangle formed by the incline. We need the hypotenuse diatance.

sin = O/H

H = O/sin

H = 34.5/sin 5

H = 396 m   which can be rounded to 400 m when considering significant figures.

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