Calculating the Length of an Incline Plane: A Kinematic Approach

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SUMMARY

The discussion focuses on calculating the length of an incline plane for a skier starting at a 15-degree angle with a final speed of 15 m/s. The participant initially attempted to use vector components and the Pythagorean theorem but was advised to apply kinematic equations for constant acceleration. The correct approach involves using the formula for distance in terms of acceleration and time, along with the sine function to determine the incline's length.

PREREQUISITES
  • Understanding of kinematic equations for constant acceleration
  • Knowledge of trigonometric functions, specifically sine and cosine
  • Familiarity with vector decomposition
  • Ability to apply the Pythagorean theorem in geometric contexts
NEXT STEPS
  • Study the kinematic equation: \(d = v_i t + \frac{1}{2} a t^2\)
  • Learn how to derive the length of an incline using trigonometric functions
  • Explore the relationship between speed, distance, and time in physics
  • Review examples of vector decomposition in physics problems
USEFUL FOR

Students studying physics, particularly those focusing on kinematics and inclined planes, as well as educators seeking to clarify these concepts for learners.

baird.lindsay
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Homework Statement


a skier starts on a hills inclined 15 degrees and the speed of the skier on the bottom of the hill is 15m/s
what is the length of the hill? and how long did it take to reach the end of the hill


Homework Equations


gsintheta , a^2+b^2 + c^2
sin=o/h


The Attempt at a Solution


i broke down the vector to components 15sintheta and 15cos theta and use pythagorean thereoum to find the slope ..would that then be the length of the hill? I am not sure how to solve to dind the time to reach the end of the hill. ...
 
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You must post your actual steps, not just a rough verbal description. Anyway, it doesn't sound right. You need to be using kinematic equations relating constant acceleration, time, and initial and final speeds. What equations can you quote like that?
 

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