Ski Slope using Energy Conservation

In summary, the question involves a skier, Julie, starting at the top of a 60 degree slope and then going through a 90 degree turn before launching off a 3.0m high ramp. The goal is to determine the horizontal distance of her touchdown point from the end of the ramp. To solve this, energy conservation and kinematics equations are used, with the mass of the skier being a non-factor. The launch angle is not specified in the question.
  • #1
merzperson
32
0

Homework Statement



It's been a great day of new, frictionless snow. Julie starts at the top of the 60 degree slope shown in the figure . At the bottom, a circular arc carries her through a 90 turn, and she then launches off a 3.0--high ramp. How far horizontally is her touchdown point from the end of the ramp?

10.P49.jpg


Homework Equations



Ug = mgh
K = 0.5mv2
Kinematics equations

The Attempt at a Solution



I know I need to use energy conservation to find the kinetic energy at the end of the ramp so I can find the velocity of the skier then, but I do not know how I can find Ug at the top of the ramp without knowing the skier's mass (too many unknowns). Once I know the initial Ug or Kmax I know how to solve the problem, but I'm having trouble getting there.
 
Last edited:
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  • #2
Never mind the mass, it will cancel. Just use m for the mass or any number you like.

ehild
 
  • #3
Thanks ehild, got it.
 
  • #4
Just wondering how the launch angle is determined in this question?
 

FAQ: Ski Slope using Energy Conservation

What is energy conservation and how does it apply to ski slopes?

Energy conservation is the practice of reducing the amount of energy used to perform a task or activity. In the context of ski slopes, energy conservation involves using efficient techniques and technologies to minimize the amount of energy required to operate the lifts, make snow, and maintain the slopes.

Why is energy conservation important for ski slopes?

Energy conservation is important for ski slopes because it helps reduce both operating costs and environmental impact. By using energy-efficient practices and equipment, ski resorts can save money on their energy bills and reduce their carbon footprint.

What are some examples of energy conservation measures that ski slopes can implement?

Some examples of energy conservation measures that ski slopes can implement include using energy-efficient snowmaking equipment, installing LED lighting, using renewable energy sources such as solar or wind power, and implementing energy-efficient building design and insulation.

How can skiers contribute to energy conservation on the slopes?

Skiers can contribute to energy conservation on the slopes by using energy-efficient techniques while skiing, such as taking efficient lines and using proper form. They can also support ski resorts that prioritize energy conservation and sustainability practices.

What are the potential benefits of energy conservation for ski resorts?

The potential benefits of energy conservation for ski resorts include cost savings, reduced environmental impact, and improved public perception and reputation. Additionally, implementing energy conservation measures can help ski resorts prepare for potential future regulations and mitigate the risks of climate change.

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