Power and Energy Problem-nothing too hard

[Oscar Wilde]

Homework Statement

"During workout, the football players at (insert generic college here) ran up the stadium stairs in 66 seconds. The stairs are 140m long and inclined at an angle of 32 degrees. If a typical player has a mass of 95 kg, estimate the average power output on the way up. Ignore friction and air resistance."

Homework Equations

w= Fd p= w/t maybe law of sin/cos perhaps p=Fv might be useful, i doubt it change in energy/time=power

The Attempt at a Solution

use law of sines to calculate that the change in height in roughly 87 meters.

Change in energy/time=power= ( 95kg*87m*10m/s^2)/(66s)=1,252 W

The correct answer was 1,000 W, and I am very frustrated. This is one of the few questions in the chapter I cannot answer. Please help, feedback appreicated

 

[mplayer]

I think you made an error in your change in height calculation. Otherwise it looks like you're doing the problem correctly. I'm getting about 1050 W for an answer.

sin(32 deg) = (h / 140m)

 

[Oscar Wilde]

Thanks! So the given "length" of the stairs is actually the hypotenuse rather than the adjacent side to the angle 32 degrees?

 

[mplayer]

Correct, the 140m is the hypotenuse. To help visualize it, you could draw it out on a graph, the positive x-axis being 0 deg. Then you can clearly see the x-component and the y-component (height), and the right triangle that these 3 lengths form.

 

[Oscar Wilde]

Thanks a lot I appreciate it, quite flustering to have something as simple as that throw off your entire solution.

Many thanks

 

[mplayer]

No problem, and don't worry about it, it happens! At least it's cleared up.