Consider a particle moving without friction on a rippled surface, given by the equation h(x) = d Cos[k x]. Gravity acts down in the negative h direction. If the particle starts at x=0 with a speed in the x direction, for what value of v will the particle stay on the surface at all times?(adsbygoogle = window.adsbygoogle || []).push({});

The answer is if v<= Sqrt[g/(k^2 d)].

I found a general formula that involves x but is too complicated to solve. There must be another way to do this without using a calculator. Thanks!

Ying

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# Lots of Forces

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