Solving the Problem of Sliding up a Ramp

[yourrock]

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.

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. :/

 

[dacruick]

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?

 

[tiny-tim]

welcome to pf!

hi yourrock! welcome to pf!

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

what do you get? ​