Solving Frictionless Snow Physics Problem - How Far from Ramp?

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SUMMARY

The discussion focuses on solving a physics problem involving a skier launching off a ramp after descending a frictionless slope. The skier starts from a height on a 60° slope and transitions through a circular arc before launching off a 3.0-meter-high ramp. The key equation used is the conservation of energy: (1/2)mv_i^2 + mgh_i = (1/2)mv_f^2 + mgh_f, leading to a calculated final velocity of 4.08 m/s. The next step involves determining the launch angle and applying projectile motion principles to find the distance from the base of the ramp to the touchdown point.

PREREQUISITES
  • Understanding of conservation of energy in physics
  • Familiarity with projectile motion concepts
  • Knowledge of basic trigonometry for angle calculations
  • Ability to apply kinematic equations
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  • Study projectile motion equations to calculate range and flight time
  • Learn how to determine launch angles using trigonometric functions
  • Explore energy conservation principles in different contexts
  • Practice similar physics problems involving slopes and ramps
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Students studying physics, particularly those focusing on mechanics, as well as educators looking for examples of energy conservation and projectile motion applications.

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Homework Statement


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

knight_Figure_10_50.jpg

Homework Equations


(1/2)mv_i^2 + mgh_i = (1/2)mv_f^2 + mgh_f

The Attempt at a Solution



I set mgh = 1/2 mv^2 + mgh
m(9.8)(25)=.5m(v^2) + m(9.8)(3)
I then got 4.08 m/s as the final velocity. But how do I figure out how far it goes if I don't know the acceleration or time?

Thanks,
 
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Once the skier leaves the ramp, the rest is a ballistics problem. You found the speed at which they fly off; what is the angle to the horizontal at which they are launched? How do you figure out what happens to the skier after that?
 

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