Ski Slope using Energy Conservation

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The discussion focuses on a physics problem involving energy conservation on a ski slope. The skier starts at a height on a 60-degree slope and launches off a ramp after a circular arc. The key equations involve gravitational potential energy (Ug = mgh) and kinetic energy (K = 0.5mv²). The main challenge is determining the initial potential energy without knowing the skier's mass, but it is noted that mass will cancel out in the calculations. The conversation also raises a question about how to determine the launch angle for the skier's trajectory after leaving the ramp.
merzperson
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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.
 
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Never mind the mass, it will cancel. Just use m for the mass or any number you like.

ehild
 
Thanks ehild, got it.
 
Just wondering how the launch angle is determined in this question?
 
Thread 'Correct statement about size of wire to produce larger extension'

Thread 'Correct statement about size of wire to produce larger extension'

The answer is (B) but I don't really understand why. Based on formula of Young Modulus: $$x=\frac{FL}{AE}$$ The second wire made of the same material so it means they have same Young Modulus. Larger extension means larger value of ##x## so to get larger value of ##x## we can increase ##F## and ##L## and decrease ##A## I am not sure whether there is change in ##F## for first and second wire so I will just assume ##F## does not change. It leaves (B) and (C) as possible options so why is (C)...
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