How Do You Calculate Initial Velocity from Jump Height?

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SUMMARY

The discussion focuses on calculating the initial velocity of a jumper based on peak jump height and standing hip position. The standing position is 100cm, the lowered hip position is 77cm, and the peak height achieved is 140cm. To find the initial velocity, the potential energy (PE) at peak height and kinetic energy (KE) formulas are utilized, specifically PE = 1/2kx² and KE = 1/2mv². The absence of time measurements complicates the calculation, but the relationship between potential and kinetic energy provides a pathway to derive the initial velocity.

PREREQUISITES
  • Understanding of potential energy (PE) and kinetic energy (KE) formulas
  • Familiarity with basic physics concepts related to motion and energy
  • Knowledge of the spring constant (k) in relation to jump height
  • Ability to manipulate algebraic equations to solve for unknowns
NEXT STEPS
  • Study the relationship between potential energy and kinetic energy in jumping scenarios
  • Learn how to calculate spring constants and their application in biomechanics
  • Explore the derivation of initial velocity from energy conservation principles
  • Investigate the effects of body mechanics on jump height and velocity
USEFUL FOR

Students in physics or biomechanics, educators teaching motion dynamics, and athletes or trainers focused on optimizing jump performance.

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Homework Statement


Standing position: 100cm
Lowered hip position: 77cm
Peak height: 140cm

Question "Use the peak height of the jump and the standing hip position to calculate the initial velocity of the jumper just after he left the ground"


Homework Equations


Unknown


The Attempt at a Solution


Unknown - I only know equations that require time. I know no time measurement in this problem.

The problem is a jumping problem. The variable above, in order, are:
1. Standing tall - from the floor to the hip
2. Crouched down to jump - from the floor to the hip
3. In mid-air at the peak of the jump - from the floor to the hip.

These were measured using a 2-meter stick.
 
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You need to use the force formulas:

PE spring = 1/2kx^2
KE = 1/2mv^2
 

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