Calculating Maximum Height in Projectile Motion for an Olympic Long Jumper

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SUMMARY

The discussion focuses on calculating the maximum height achieved by an Olympic long jumper who jumps 8.5 meters with an initial horizontal velocity of 9.7 m/s. The participant initially calculated the time of flight as 0.88 seconds and attempted to use the equation Y = Yinitial + Vyinitial*t - 0.5at^2 to find the maximum height. After several incorrect attempts, it was concluded that the initial vertical velocity (Vyinitial) was miscalculated, leading to erroneous height results. The correct approach involves determining Vyinitial using the equation Vf = Vi + at before applying it to the height calculation.

PREREQUISITES
  • Understanding of kinematic equations in physics
  • Familiarity with projectile motion concepts
  • Knowledge of vertical motion under gravity, specifically acceleration due to gravity (-9.80 m/s²)
  • Ability to manipulate algebraic equations for solving physics problems
NEXT STEPS
  • Learn how to derive initial vertical velocity (Vyinitial) from horizontal motion data
  • Study the application of kinematic equations in projectile motion scenarios
  • Explore the concept of time of flight in projectile motion
  • Practice solving similar projectile motion problems with varying initial conditions
USEFUL FOR

Students studying physics, educators teaching projectile motion, and anyone interested in understanding the calculations behind athletic performance in long jumping.

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Homework Statement


An Olympic long jumper is capable of jumping 8.5 m. How high does he goes? (Assuming he lands standing upright). His initial horizontal velocity is 9.7 m/s.

Before it asked his height, I found that the time he is in the air is 0.88 seconds.


Homework Equations


Y=Yinitial+Vyinitial*t-.5at^2


The Attempt at a Solution


Since Y is the maximum height, I just tried plugging in numbers for the symbols in the rest of the equation. Yintial was 0, Vyintial was 0, t was 0.44 because max height is in the middle, and a is -9.80m/s2. I got an answer of 9.5, which was wrong. I have a feeling I'm substituting incorrectly but can't figure out what.
 
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The assumption that Vy initial is zero is wrong. If it was zero, then the maximum height would be zero.

It seems to me you would have to use Vf = Vi + at to find Vi before doing your vertical distance calc.
 
Ok, so hoping my calculations for Vy initial are correct, I got 18 m/s, then I tried finding the maximum height and got 20 meters with time as 0.88, which was incorrect. So I thought I should put in time as 0.44 because that is when he will be at maximum height and got 8.9 and that was incorrect too. Not sure what to do now.
 
I think 18 is much too large for Vy initial. It would be more helpful if you showed what you did than what the answer was. I used
Vf = Vi + at
-Vi = Vi -9.8*t
2*Vi = 9.8*0.88
 

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