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 !)