One dimensional motion problem

[Amar.alchemy]

1. The problem statement, all variables and given/known data
Challenge Problem(2.96) from University Physics text book:
In the vertical jump, an athlete starts from a crouch and jumps upward to reach as high as possible. Even the best athletes spend little more than 1.00s in the air (their "hang time"). Treat the athlete as a particle and let Ymax 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 y/2 to the time it takes him to go from the floor to that height. You may ignore air resistance.

2. Relevant equations
constant acceleration equations: y=Y0 + V0t - 4.9t2....1
V2y=V20y-2g(y-y0)......2

3. The attempt at a solution
Part 1(Time it takes him to go from floor to Ymax /2):
ay= -g, origin at the floor, V0y=0, y=Ymax /2, y0=0

so if i substitute these known quantities in the second equation, then for the velocity at the position Ymax /2 i am getting complex roots. Kindly inform me where i am going wrong.

Thanks,

[womfalcs3]

Try using a positive value for g. Since when you ultimately calculate time, using a negative value would result in a negative value under the square root.

Edit: Strike out what I said.

[Cyosis]

No. if v0y=0 then how can he even get into the air? You can calculate what v0y is because you know what vymax is. What is vymax?

[Amar.alchemy]

No. if v0y=0 then how can he even get into the air? You can calculate what v0y is because you know what vymax is. What is vymax?

Thanks Cyosis, I got it. since we know that Vymax is zero we can calculate the initial velocity of the part 2 which becomes the final velocity of part 1. am i right??

[Cyosis]

Yep.