When jumping, a flea accelerates at an astounding 1500 m/s^2, but over only the very short distance of 0.48mm. If a flea jumps straight up, and if air resistance is neglected (a rather poor approximation in this situation), how high does the flea go?

Given the fleas acceleration over a known distance you can find it's initial velocity from v^2 = 2ad. Then the height it rises given that initial velocity can be found from v^2 = 2gh. Solve for h.