Exercise Program Homework: Calculating Jumps & Time Needed

[Emethyst]

Homework Statement

A 75kg person is put on an exercise program by a physical therapist, the goal being to burn up to 500 food calories in each daily session. Human muscles are about 20% efficient in converting energy into mechanical energy. The exercise program consists of a set of consecutive high jumps, each one 50cm into the air and lasting 2s. How many jumps should the person do per session, and how much time should be set aside for each session?

Homework Equations

Kinetic energy, potential energy, conservation of energy

The Attempt at a Solution

I tried to solve this by first finding the potential energy of the person, and then using this value to calculate the energy burned by multiplying it by 0.20. Afterwards, I divided 2092J (obtained by converting the 500 food calories into joules) by the energy burned. The value I obtained was much too small, so I know I'm going wrong somewhere, I just don't know where, although I think I might have converted the food calories wrong. If anyone can point me in the right direction here it would be greatly appreciated, thanks in advance.

 

[mgb_phys]

Remember a food calorie is really 1000 calories (ie 1kcal)
so 1 joule = 2.3901×10^−4 kcal or 1 kcal is about 4184 joules

 

[Emethyst]

Ahh I thought I converted it wrong, thanks for pointing out my mistake, however, if I use the new value that gives me, I get an answer too large (2.85x10^4 when it should be 1.1x10^3); is there some other place I'm going wrong here?