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Solved: In the vertical jump, an athlete starts from a
Chapter 2, Problem 96CP(choose chapter or problem)
Problem 96CP
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 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 ymax/2 to the time it takes him to go from the floor to that height. Ignore air resistance.
Questions & Answers
QUESTION:
Problem 96CP
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 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 ymax/2 to the time it takes him to go from the floor to that height. Ignore air resistance.
ANSWER:
Solution to 96 CP
When an athlete jumps up in the air, he uses all his strength to reach the maximum height.
Step 1
Suppose he takes t time to reach the maximum height ymax. Then initial velocity of the athlete is taken as u and the final velocity, v=0 at the highest point.
From equations of motion,
v=u-gt
t=(u/g)seconds
Thus the athlete would remain in the air for t seconds. As initial velocity increases, more height would be reached, thus athlete will remain in the air for a longer duration. This is why athlete seems to be hung in the air for short duration.