Question

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

Answer 1

 
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 !)