Gravitational potential energy of skier

In summary, a 78.9-kg skier rides a 3150-m-long lift to the top of a mountain at an angle of 11.9° with the horizontal. The change in the skier's gravitational potential energy can be found using the equation GPE = mgh, where h is the height. To find the height, we can use the formula h = d*sinθ, where d is the distance and θ is the angle. After substituting the values, the skier's GPE is calculated to be 502,237.3J.
  • #1
kittymaniac84
17
0

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[tex]\theta[/tex](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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  • #2
First of all, the skier is going UP the mountain. Should his gravitational potential increase or decrease?
 
  • #3
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?
 
  • #4
oh, so the height would be 3150*sin11.9= 649.54m

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

Is that right?
 
  • #5
Assuming the skier started at height 0, then that answer looks right to me.
 
  • #6
that was correct..thanx!
 

1. What is gravitational potential energy of a skier?

The gravitational potential energy of a skier is the energy that is stored in the skier's position in relation to the Earth's surface due to the force of gravity.

2. How is the gravitational potential energy of a skier calculated?

The gravitational potential energy of a skier can be calculated by multiplying the skier's mass by the acceleration due to gravity (9.8 m/s²) and the height of the skier's position above the ground.

3. Why is gravitational potential energy important for skiers?

Gravitational potential energy is important for skiers because it affects their speed and trajectory while skiing. As the skier moves downhill, their potential energy is converted into kinetic energy, which determines how fast they are skiing.

4. How does the height of a skier affect their gravitational potential energy?

The higher a skier is positioned above the ground, the greater their gravitational potential energy will be. This is because the skier has more potential to gain kinetic energy as they ski downhill.

5. Can the gravitational potential energy of a skier be changed?

Yes, the gravitational potential energy of a skier can be changed by altering their position in relation to the ground. If the skier moves to a higher position, their potential energy will increase, and if they move to a lower position, their potential energy will decrease.

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