Skier at the top of a hill

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In summary, the skier starts from rest at the top of a hill and coasts down and up a second hill with a circular crest of radius 38.5m. Neglecting friction and air resistance, the height of the first hill (h) is equal to half the radius of the second hill (r). The equation used to find this was mgh=1/2mgr.
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Homework Statement

A skier starts from rest at the top of a hill. The skier coasts down the hill and up a second hill,The crest of the second hill is circular, with a radius of r = 38.5m. Neglect friction and air resistance. What must be the height h of the first hill so that the skier just loses contact with the snow at the crest of the second hill?

Homework Equations

ke=1/2mv^2 and pe=mgh
e=pe+ke


The Attempt at a Solution

e=0 so pe =ke and h=(H-2r) and v^2=gr
so i found h=2r+r/2 and i got 96.25 m but its not right please help
 
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ok wait i think i found my problem it should be mgh=1/2mgr so h=1/2r...
 

Related to Skier at the top of a hill

1. What is the potential energy of a skier at the top of a hill?

The potential energy of a skier at the top of a hill is equal to their mass multiplied by the acceleration due to gravity (9.8 m/s^2) and the height of the hill.

2. How does the height of the hill affect the potential energy of the skier?

The higher the hill, the greater the potential energy of the skier at the top. This is because the potential energy is directly proportional to the height of the hill.

3. What is the relationship between potential energy and kinetic energy for a skier at the top of a hill?

At the top of the hill, the skier has only potential energy. As they start to ski down the hill, their potential energy decreases and their kinetic energy increases. At the bottom of the hill, all of their potential energy is converted into kinetic energy.

4. How does the weight of the skier affect their potential energy at the top of the hill?

The weight of the skier affects their potential energy at the top of the hill because it is directly proportional to their mass. The greater the mass of the skier, the greater their potential energy will be.

5. Is there any other factor that can affect the potential energy of a skier at the top of a hill?

Apart from mass and height of the hill, the only other factor that can affect the potential energy of a skier at the top of a hill is the acceleration due to gravity. This is a constant value and cannot be changed by the skier.

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