Re: [Phys-L] quickest route

[David Bowman <David_Bowman@georgetowncollege.edu>]

Regarding Bob's comment:

> 37.8 degrees gives a correspondence to 3 significant figures -
> Excel quickie check. The condition for equal times is
> 1 + 1/(2cos(theta)=1/sin(theta).

Ah, so that's the problem.  Your equal time condition above is
incorrect.  If you replaced your cosine function by a tangent
function in the above equation then your equal time condition
would be correct.  The only reason your answer differed from the
correct one by only about a degree or so is that the cosine
function and the tangent function have nearly the same value at
about 38 degrees. (Actually, the cosine and tangent function have
the exact same value at the arcsine of the reciprocal of the
golden mean.)

Dave Bowman