# Needed Power Output on an Incline

1. Oct 9, 2008

### akfortyseven

1. The problem statement, all variables and given/known data
A bicyclist coasts down a 7 degree hill at a steady speed of 5 m/s. Assuming the total mass of 75 kg, what must be the cyclist's power output to climb the same hill at the same speed

2. Relevant equations
power = force * distance / time
force of gravity = mass * gravity

3. The attempt at a solution
At first glance, I just did 75 kg * 9.8 m/s^2 * 5 m * sin(7 degrees) / 1 s, which equaled to about 448 W
But the problem is, if the cyclist was on flat ground, the he/she would need an output of 3675 W, which is far greater 448 W
So then I tried 83 degrees since 90-7=83
When I replaced 7 degrees with 83, I got an output of about 3648 W, which sounds more reasonable to me.
Which answer is right? If neither of them are, what can help me to get the right answer?

2. Oct 9, 2008

### Hootenanny

Staff Emeritus
I would say that your first answer is correct. I'm not sure where your pulling the 3675W on the flat from.

3. Oct 9, 2008

### akfortyseven

I got it from the situation if the cyclist was going at 5 m/s on flat ground with no incline