In the Empire State Building Run-up, participants compete to see who can run up the 320 m Empire State Building the fastest. The current record holder, Paul Crake, who has a mass of 64 kg, covered this distance in 9 min and 33 s. What is the minimum average output power that his body produced while doing this?

Wow! I'll betcha his mass was not still 64 kg when he got to the top.

In raising the mass of 64 Kg to 320 m above the street,

the mass gained gravitational potential energy equal to

m G h = (64 kg) (9.8 m/s²) (320 m)

= 200,704 joules.

9 minutes 33 seconds is equivalent to

(9 min x 60 sec/min) + (33 sec)

= 540 sec + 33 sec = 573 seconds.

Power = (energy) / (time) = (200,704 joules) / (573 sec) = 350.3 watts

That's pretty nearly 1/2 horsepower (0.47), and he kept it up for almost 10 minutes.

Wotta guy!

Power can be calculated using the following rule:

Power = work / time

So, first we need to calculate the work done. Work can be calculated using the following rule:

W = mass * gravity = 64 * 9.8 * 320 = 200704 joules

We are given that the time is 9 minutes and 33 seconds. That is equal to 9 (60) + 33 = 573 seconds

Substitute with the work and time in the equation of power to get the value of the power as follows:

P = (200704) / (573) = 350.2687609 watt