# Power - biking uphill

1. Oct 16, 2008

### Symstar

1. The problem statement, all variables and given/known data
A bicyclist coasts down a 6.0 degree hill at a steady speed of 4.5 m/s.
Assuming a total mass of 60 kg (bicycle plus rider), what must be the cyclist's power output to climb the same hill at the same speed?

2. Relevant equations
Newton's 1st law
P=W/t

3. The attempt at a solution
$$P=\frac{W}{t}=F \cdot v$$

Set x-axis along incline...
$$F-mg\sin\theta=0$$
$$F=mg\sin\theta$$
$$P=mg\sin\theta*4.5 = 276.6 W$$

To 2 sigfig = 280 W

Is this correct? I'm being told it is the wrong answer...

2. Oct 16, 2008

### nasu

It looks right.
Who told you that is not?

3. Oct 16, 2008

### Symstar

The site where I submit my homework =/ I can't find any problem with it either, so I dunno whats up - guess I'll go ask the professor tomorrow. Thanks for checking my work and please let me know if you do think of somewhere I went wrong.

4. Oct 17, 2008

### Symstar

Just an update... since the rider coasts down the hill but isn't accelerating, we must assume that there is a retardant force which must also be factored in when going uphill. This is where I went wrong. Kind of a trick question... blah!