How Do You Calculate Initial Velocity from Jump Height?

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To calculate the initial velocity of a jumper from jump height, the peak height of 140 cm and the standing hip position of 100 cm are essential variables. The problem involves understanding the transition from potential energy (PE) at peak height to kinetic energy (KE) just after takeoff. The relevant equations include PE = 1/2kx^2 and KE = 1/2mv^2, although time measurements are not provided. The challenge lies in applying these formulas without direct time data. Ultimately, the solution requires relating the height difference to the initial velocity using energy conservation principles.
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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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