Gravitational Potential Energy of a vehicle

[Winegar12]

Homework Statement

An all-terrain vehicle with a 2,000 kg mass moves up a 15^o slope at a constant velocity of 6 m/s. What is the rate of change of gravitational potential energy with time?

Homework Equations

W=\DeltaE/\Deltat
W=FXd
Ki+Ui=Ki+Ui (I think that's what it is)
Pe=mgh
1/2mv²=

The Attempt at a Solution

Ok I'm pretty sure those are the equations we need to use. I know what the answer is and it is in Watts. However I have tried a million things to try and get the answer but I can't seem to get it. I'm assuming that in the equation Pe=mgh, the h would change to sin\theta. To be honest, I've tried it a few different ways and can't seem to get it. I'm sure I'm overthinking it, I just need some nudge in the right direction.

 

[p21bass]

You have one of the correct equations, in PE = mgh. And yes, you have to factor in sin(theta). All of the other equations, though, aren't necessary. Since you obviously know that PE is proportional to the height - what you really need to know is how the height changes over time. Then use that information to answer the question.

 

[Winegar12]

So obviously there is another equation that I need to use obviously...any nudge on what the equation I would use? Will I be using a type of Trig equation? You said that I would need to factor in sin(theta) but I still need the height. So I won't replace the height with sin(theta), but will still use it in the equation. For example would I do, Pe =mghsin(theta) and just times them all together. The answer is a large number so I'm assuming that's what I would do...

 

[p21bass]

Almost - it won't be PE=mghsin(theta), as what you need to do is find h as a function of the distance it's traveled on the incline and sin(theta) - which is a basic trig function. Then, choose a time interval (I'd suggest 0s and 1s) and compare the two PEs.