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)²Divide each side by gravity:                      Height = (1/2) (121 m²/s²) / (9.8 m/s²)                                =  6.173 meters                         (about  20.3 feet !)