MathDB

Suppose we climb a mountain that is a cone with radius

100

and height

4

. We start at the bottom of the mountain (on the perimeter of the base of the cone), and our destination is the opposite side of the mountain, halfway up (height

z = 2

). Our climbing speed starts at

v_0=2

but gets slower at a rate inversely proportional to the distance to the mountain top (so at height

z

the speed

v

(h-z)v_0/h

). Find the minimum time needed to get to the destination.

Problem Statement