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Amar.alchemy
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Homework Statement
Challenge Problem(2.96) from University Physics textbook:
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.
Homework Equations
constant acceleration equations: y=Y0 + V0t - 4.9t2...1
V2y=V20y-2g(y-y0)...2
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,