A flea is able to jump straight up about 0.58 m. It has been said that if a flea

Question

A flea is able to jump straight up about 0.58 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 1045, the cross section of its muscle would increase by 10452 and the length of contraction would increase by 1045. How high would this "super flea" be able to jump? (Don't forget that the mass of the "super flea" increases as well.)

Explanation / Answer

The work done by flea is Wo = mo*g*ho
Work done by superflea is W1 = m1*g*h1
.From the above...
h1 / ho = (W1 / m1*g) * (mo*g / Wo)
.
h1 = ho * (W1 / Wo) * (mo / m1) but W = f * d
h1 = ho * [(f1 * d1) / (fo / do)] * (mo / m1)
Now f1= 1092025 * fo, and
d1 = 1045 * do
m1 = 1045^3 * mo
h1 = ho * 1092025 * 1045/ 1141166125
h1 = ho = 0.58 m

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