Question

an Olympic runner leaps over a hurdle.if the runner initial vertical speed is 2.2m/s how much will the runners center of mass be raised during jump?

Answer 1

Supposing the runner is condensed to a point and moves upward at 2.2 m/s.
It takes a time = 2.2/g = 2.2/9.8 = 0.22 seconds to increase to max height. 
Now looking at this condition in opposite - that is the runner is at max height and drops back to earth in 0.22 s (symmetry of this kind of motion). 
From what height does any object take 0.22 s to fall to earth (supposing there is no air friction)? 
d = 1/2gt²= (0.5)(9.8)(0.22)²= 0.24 m