### How high would this superflea be able to jump

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A flea is able to jump straight up about 0.56 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 550, the cross section of its muscle would increase by 5502 and the length of contraction would increase by 550. How high would this "superflea" be able to jump? (Don't forget that the mass of the "superflea" increases as well.)

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