Gravitational potential energy of skier

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Homework Help Overview

The discussion revolves around calculating the change in gravitational potential energy for a skier using the height gained from a ski lift. The problem involves understanding the relationship between the angle of the lift and the vertical height achieved.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the correct application of angles in calculating height and gravitational potential energy. Questions arise regarding the use of the angle in the formula and whether the skier's potential energy should increase or decrease.

Discussion Status

Some participants have provided guidance on the correct formula for gravitational potential energy and how to derive height from the angle of the lift. There is an ongoing exploration of the implications of the angle used in calculations, with some participants confirming the correctness of the height calculation.

Contextual Notes

Participants are discussing the assumptions regarding the starting height of the skier and the implications of using different angles in their calculations. There is a focus on ensuring clarity between gravitational potential energy and work done.

kittymaniac84
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Homework Statement



A 78.9-kg skier rides a 3150-m-long lift to the top of a mountain. The lift makes an angle of 11.9 ° with the horizontal. What is the change in the skier's gravitational potential energy?

Homework Equations



W=mgcos\theta(ho-hf)

The Attempt at a Solution



W=78.9*9.8*cos11.9*(0-3150)=-264,810.95J

I am confused if the angle i used was correct or should i subtract it from 90 or something. I tried that and it was still wrong. Can someone tell me what I am doing wrong? is the angle used right
 
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First of all, the skier is going UP the mountain. Should his gravitational potential increase or decrease?
 
Another note, although they are the same units, you are looking for gravitational potential energy, not work, so your formula isn't quite right.

GPE = mgh

So, you need to find 'h'. If the angle is 11.9˚ with the horizontal, how would you find the height?
 
oh, so the height would be 3150*sin11.9= 649.54m

GPE= 78.9*9.8*649.54=502,237.3J

Is that right?
 
Assuming the skier started at height 0, then that answer looks right to me.
 
that was correct..thanx!
 

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