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?

DanielCai Mar 28, 2019

#1**+1 **

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

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?

Rom Mar 28, 2019