Solving the Problem of Sliding up a Ramp

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SUMMARY

The discussion centers on optimizing the distance D for a cart sliding down a frictionless ramp with a height of 2.8 m and a length of 5.1 m. Participants suggest using standard constant acceleration equations to derive time and speed as functions of D. The goal is to determine the optimal D that minimizes the time taken for the cart to reach the end of the track. Collaboration among classmates indicates a common challenge in solving this physics problem.

PREREQUISITES
  • Understanding of kinematics and constant acceleration equations
  • Familiarity with frictionless motion concepts
  • Basic knowledge of physics principles related to ramps and inclined planes
  • Ability to perform algebraic manipulations to solve equations
NEXT STEPS
  • Study the equations of motion for constant acceleration
  • Explore the principles of energy conservation in frictionless systems
  • Learn how to derive time and speed functions from distance in physics problems
  • Investigate optimization techniques in calculus for minimizing time
USEFUL FOR

Students studying physics, particularly those focusing on kinematics and motion on inclined planes, as well as educators looking for collaborative problem-solving strategies in physics coursework.

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Homework Statement



A frictionless track is to be built as shown, with L= 5.1 m and H= 2.8 m. In order to get the cart to slide from the top to the end of the track in the minimum time, how long should the distance D be? Assume that the speed of the cart on the horizontal surface is the same as at the bottom of the ramp.

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Homework Equations





The Attempt at a Solution



This is the problem given to me as homework, I discussed it with a lot of my classmates but no one is seem to be able to solve it. If I can't get an answer as a last resort I'll go see my teacher. :/
 
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Well what is your attempt at a solution? What have you tried so far? At the very least, what have you discussed with your classmates?
 
welcome to pf!

hi yourrock! welcome to pf! :wink:

use the standard constant acceleration equations to find the time and the speed (all as functions of D) …

what do you get? :smile:​
 

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