- #36
pbuk
Science Advisor
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- You have confused things greatly by putting ## t ## in your equations to represent an angle which you have called theta. It would be much clearer if you had used ## \theta ## (i.e.
## \theta ##
to mean theta leaving ## t ## for time. - Where did you get ## Time = sqrt(r/g) * dt ## from? What does it mean? Does ## dt ## here have something to do with time?
- How do you know that your assumption that the optimal curve when the initial velocity is non-zero is a cycloid is correct?
- You have not specified the final velocity anywhere, can it be zero?
You start talking about depth and elsewhere you mention a distance of 5,000 metres. Do you realize that gravity decreases with depth? (edit: oops, no it doesn't!)- Do you realize that friction, and particularly air resistance, becomes very significant at increased velocity, meaning that for any real application you need to provide additional power to avoid falling short of the destination and falling back down the slope?
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