Solving a Ski Slope: Length & Time for Descent

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Homework Help Overview

The problem involves a skier transitioning from horizontal motion to descending a 10-degree incline, with given initial and final speeds. The questions focus on determining the length of the incline and the time taken to descend.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the forces acting on the skier, particularly the role of gravity and its components along the incline. There are attempts to derive the acceleration using trigonometric relationships from a free body diagram.

Discussion Status

Some participants have provided insights into the forces involved and suggested using a free body diagram to analyze the situation. There is an ongoing exploration of the correct approach to calculating acceleration, with differing interpretations of the gravitational force's effect on the skier.

Contextual Notes

Participants express concern about the accuracy of their calculations and the implications for an upcoming exam, indicating a time constraint and the need for clarity in understanding the physics involved.

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Homework Statement


A skier is gliding along at 3m/s on horizontal frictionless snow. He suddenly starts down a 10 degree incline. His speed at the bottom is 15 m/s.
a) what is the length of the incline?
b) how long does it take for him to reach the bottom?
we know:
Vo=3m/s
Vf=15m/s
t=?
x=?
a=?

Homework Equations


V^2=Vo^2 +2ax



The Attempt at a Solution


i need help to find what the a is...and why it is that.
 
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the only force acting on the skier is gravity but since the skier is going down a 10 degree incline gravity is giving him some acceleration but not 100% of it's full foce.

draw the Free Body Diagram and split up gravity into it's components where the acceleration will be parallel to the incline.
 
okay from my freebody diagram i get sin(10)=9.8/a
a=56.4
and that is wrong...if anyone could explain to me how to do it properly please...id greatly appreciate it because i have my exam very soon.
 
it should be 9.8*sin(10). the force acting parallel to the inclined plane is mgsin(theta).
 

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