The worlds 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 with the sprinter need to climb

What a delightful little problem!

- - When he is running on level ground, his kinetic energy is

KE = (1/2) x (mass) x (speed) ².

- - When he climbs up from the ground, his potential energy is

PE = (mass) x (gravity) x (height above the ground).

We're looking for the height that makes these quantities of energy equal,

figuring that when he runs, his speed is 11 m/s.

The first time I looked at this, I thought we would need to know the runner's

mass. But it turns out that we don't.

PE = KE

(mass) x (gravity) x (height) = (1/2) (mass) (11 m/s) ²

Divide each side by (mass):

(gravity) x (Height) = (1/2) (11 m/s) ²

Divide each side by gravity:

Height = (1/2) (121 m²/s²) / (9.8 m/s²)

= 6.173 meters

(about 20.3 feet!)