Burning Off" 200 Cal: How High Must Student Climb?

[holoforce]

Homework Statement

A 100-kg student eats a 200-Calorie doughnut. To "burn it off", he decides to climb the steps of a tall building. How high (in m) would he have to climb to expend an equivalent amount of work? (1 food Calorie = 103 calories.)

Homework Equations

W = Fd

The Attempt at a Solution

d = W/F
= (200 x 103 cal)(4.186 J/cal) / (100kg)(9.8m/s2)
= 87.99m

The solution says its 854m which doesn't make sense to me at all.

 

[rock.freak667]

I would go with your answer. Running almost a kilometer just burn off 1 donut seems weird.

 

[phyzguy]

In fact one food calorie = 10^3 =1000 calories, not 103 calories. The 854m is the correct answer. Of course, this assumes that your body is 100% efficient at turning food energy into mechanical energy, which it isn't, but that is probably what you are supposed to assume for this problem.