Quote:
Originally Posted by Richard
If the speed function has the same form as that of the unpowered object, namely the inverse square root of the object's gravitational potential, then the curve of quickest ascent will be a cycloid.
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In other words, no.
:-)
For high-school students interested in math and/or physics, the attachment shows how to use high-school-level calculus to figure out the travel time from point A to point B for a particle sliding down an arbitrary frictionless curve. You can replace f(x) with a straight line or a parabola or a cycloid or whatever and see the difference.