grae313 wrote:It seems to me like the OP is not so interested in his ability to get the question right using the quickest method--he did that successfully--he's curious aside from any practical concerns if there is a quick, analytical solution involving derivatives...
quizivex wrote:Yea, it's always more instructive to know the "solution", not just that the answer is correct. But beware that some of the problems on the GRE would be suicidal to attempt analytically. I recall one practice test problem asking which formula represents the modes of vibration of a string fixed at one end with a mass M at the other... Even if you knew how to derive it from DEQ's, testing M->0 and M->infinity was the only way to get the answer in a reasonable amount of time.
As for your problem:
You know the tangential acceleration (TA) is the tangential component of m*g. If theta is the angle the curve makes with the vertical, you get:
cos(theta) = TA / mg
You also know you can relate the tangent of the angle with the slope of the track. In this case, tan(theta) = dx/dy = 1/(dy/dx)
Now relate tan() and cos() using trig, do some substitution and get the answer. (I think...)
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