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An ant travels from the point \(A (0,-63)\) to the point \(B (0,74)\) as follows. It first crawls straight to (x,0) with x>=0, moving at a constant speed of \(\sqrt 2\) units per second. It is then instantly teleported to the point (x,x). Finally, it heads directly to B at 2 units per second. What value of x should the ant choose to minimize the time it takes to travel from A to B?

 Mar 28, 2019

\(T =\dfrac{\sqrt{x^2+63^2}}{\sqrt{2}} + \dfrac{\sqrt{x^2 + (74-x)^2}}{2} s\)


What class is this?  Are you allowed to use calculus to minimize this?


If not there's a ton of messy algebra to convert T into parabolic form and choose the vertex as the minimum.


You use the word geometry.  Are you supposed to come up with a geometric solution?

 Mar 28, 2019

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