Question

A champion athlete can produce one horsepower (746 w) for a short period of time. if a 70-kg athlete were to bicycle to the summit of a 500-m high mountain while expending power at this rate, she would have used at least ____ j of energy.

Answer 1

The energy the athlete has the use to ride to the summit of the hill is equal to the increase in gravitational potential energy of the athlete:

`\Delta U= mg \Delta h`

where m is the mass of the athlete, g is the gravitational acceleration and
`\Delta h` is the height of the top of the hill with respect to the ground.

In this problem,
`m=70 kg`,
`g=9.81 m/s^2` and
`\Delta h=500 m`, therefore the minimum energy the athlete must use is

`\Delta U=(70 kg)(9.81 m/s^2)(500 m)=3.43 \cdot 10^5 J`