Skier coasts down hill speed at bottom?

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SUMMARY

The discussion centers on calculating the speed of a skier at the bottom of a 10 m high slope, starting with an initial speed of 5.0 m/s. The relevant equations for kinetic energy (KE = 1/2 mv²) and potential energy (PE = mgy) are established as foundational tools for solving the problem. Additionally, the impact of friction, quantified as 2500 J of work done against the skier, is considered in determining the final speed. The conservation of energy principle is applied, indicating that the total mechanical energy at the top equals the total mechanical energy at the bottom, minus the work done by friction.

PREREQUISITES
  • Understanding of kinetic energy (KE) and potential energy (PE) equations
  • Basic knowledge of the conservation of energy principle
  • Familiarity with the concept of work done against motion
  • Ability to perform algebraic manipulations to solve for unknowns
NEXT STEPS
  • Calculate the final speed of the skier using the conservation of energy principle
  • Explore the effects of varying mass and height on the skier's speed
  • Investigate the role of friction in energy loss during motion
  • Learn about energy transformations in different physical scenarios
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Students studying physics, particularly those focusing on mechanics and energy conservation, as well as educators seeking to explain these concepts in practical scenarios.

araspante
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Hello! Just wondering if anyone could point me in the correct direction with these problems?

Homework Statement


"A skier coasts down a very smooth, 10 m high slope. If the speed of the skier on the top of the slope is 5.0 m/s, what is his speed at the bottom of the slope?"

and...

"If the skier has a mass of 60 kg, and the force of friction retards his motion by doing 2500 J of work, what is his speed at the bottom of the slope?"


I just can't seem to figure out what equation to use to figure this out.
Help!

Thanks SO much!
 
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welcome to pf.
At the top of the hill the skier has kinetic and potential energy - at the bottom he has just kinetic - since no energy is lost these are equal.
what are the equations for KE and PE?
 
thank you!

the equations are...

KE= 1/2mv^2
PE= mgy
 

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