Solving the Superflea Jump Problem: How High Can it Jump?

[sam_hall88]

A flea is able to jump straight up about 0.51 m. It has been said that if a flea were as big as a human, it would be able to jump over a 100 story building! When an animal jumps, it converts work done in contracting muscles into gravitational potential energy (with some steps in between). The maximum force exerted by a muscle is proportional to its cross-sectional area, and the work done by the muscle is this force times the length of contraction. If we magnified a flea by a factor of 500, the cross section of its muscle would increase by 500^2 and the length of contraction would increase by 500. How high would this "superflea" be able to jump? (Don't forget that the mass of the "superflea" increases as well.)
? m
How do I get started on this problem?

 

[mgb_phys]

Here is a good start: http://fathom.lib.uchicago.edu/2/21701757/