Solving a Ski Slope: Length & Time for Descent

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SUMMARY

The discussion focuses on calculating the length of a ski slope and the time taken for a skier to descend it, given an initial speed of 3 m/s and a final speed of 15 m/s on a 10-degree incline. The key equations used include the kinematic equation V^2 = Vo^2 + 2ax, where the acceleration (a) is derived from the gravitational force component acting parallel to the incline. The correct formula for acceleration is a = g * sin(θ), where g is 9.8 m/s² and θ is the incline angle.

PREREQUISITES
  • Understanding of kinematic equations
  • Basic knowledge of trigonometry, specifically sine functions
  • Familiarity with free body diagrams
  • Concept of gravitational force components
NEXT STEPS
  • Calculate the length of the incline using the derived acceleration and kinematic equations
  • Determine the time taken to reach the bottom using the equation t = (Vf - Vo) / a
  • Explore the effects of different incline angles on acceleration and descent time
  • Review concepts of dynamics related to inclined planes and frictionless motion
USEFUL FOR

Students preparing for physics exams, particularly those studying mechanics and inclined plane problems, as well as educators looking for practical examples of kinematic equations in action.

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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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