Solving the Problem of Sliding up a Ramp

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To solve the problem of a cart sliding down a frictionless ramp, the key is to determine the optimal distance D that minimizes the time taken to reach the end of the track. The discussion emphasizes using standard constant acceleration equations to derive time and speed as functions of D. Participants express difficulty in finding a solution and consider seeking help from a teacher if needed. Collaboration among classmates has not yielded results, indicating the complexity of the problem. Ultimately, applying physics principles is crucial to finding the answer.
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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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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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