In the vertical jump, an athlete starts from a crouch and jumps upward as high as possible. Even the best athletes spend little more than 1.00 s in the air (their ""hang time""). Treat the athlete as a particle and let [math]y_{\max }[/math] be his maximum height above the floor. To explain why he seems to hang in the air, calculate the ratio of the time he is above [math]y_{\max } / 2[/math] to the time it takes him to go from the floor to that height.