Solving Frictionless Snow Physics Problem - How Far from Ramp?

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Julie starts at the top of a 60-degree slope and launches off a 3.0-meter-high ramp after navigating a circular arc. The energy conservation equation is applied to find her final velocity at the ramp's edge, resulting in a speed of 4.08 m/s. The discussion shifts to determining the projectile motion after leaving the ramp, focusing on the launch angle and its impact on the distance traveled. The key challenge is calculating how far she will land from the base of the ramp without knowing acceleration or time. The problem ultimately requires applying principles of ballistics to solve for the touchdown point.
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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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