Kinetic and potetnial energy in a circle?

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SUMMARY

The discussion focuses on calculating the final velocity of a person swinging from a height of 3.80 m before entering the water. Using the conservation of energy principle, the equation KEf + PEf = KEo + PEo is applied. The calculated final velocity (Vf) upon release is determined to be 13.7 m/s, derived from the kinetic and potential energy equations. The problem ignores air resistance, simplifying the calculations.

PREREQUISITES
  • Understanding of kinetic energy (KE) and potential energy (PE) concepts
  • Familiarity with the conservation of energy principle
  • Basic algebra for solving equations
  • Knowledge of gravitational acceleration (9.8 m/s²)
NEXT STEPS
  • Study the derivation of the conservation of energy equation in physics
  • Learn about the effects of air resistance on projectile motion
  • Explore advanced applications of kinetic and potential energy in real-world scenarios
  • Investigate the relationship between height and velocity in free fall
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Students studying physics, educators teaching energy concepts, and anyone interested in mechanics and motion analysis.

TheBowl3r
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Homework Statement


The drawing below shows a person who, starting from rest at the top of a cliff, swings down at the end of a rope, releases it, and falls into the water below. There are two paths by which the person can enter the water. Suppose he enters the water at a speed of 10.0 m/s via path 1. How fast is he moving on path 2 when he releases the rope at a height of 3.80 m above the water? Ignore the effects of air resistance.


Homework Equations


KEf+PEf=KEo+PEo
KE=1/2mv^2
PE=mgh

The Attempt at a Solution


KEf=KEo+PEo-PEf
Vf=sqr(2((.5*Vo)+(9.8*10)-(9.8*3.8)))
Vf=13.7m/s
 
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