At the ground, the kinetic energy is:

$\overline{){\mathbf{K}}{\mathbf{E}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{m}}{{\mathbf{v}}}^{{\mathbf{2}}}}$

Above the ground, the potential energy is:

$\overline{){\mathbf{P}}{\mathbf{E}}{\mathbf{=}}{\mathbf{m}}{\mathbf{g}}{\mathbf{h}}}$

Equate the two equations:

PE = KE

mgh = (1/2)mv^{2}

The world's fastest humans can reach speeds of about 11 m/s.

In order to increase his gravitational potential energy by an amount equal to his kinetic energy at full speed, how high would such a sprinter need to climb?

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