Problem 52839. Easy Sequences 33: Web Trapped Ant
An ant is trapped on a spider web inside a can with open top. The can has a radius R and height H. A spider sitting on the outside face of the can, sensed the trapped ant and started crawling towards it. The relative positions of the ant and spider are shown in the figure below.
is the initial distance of the spider from the from the bottom of the can, is the distance of the ant from the top of the can, and and , are the y-offsets of the spider and ant, respectively, from the center of the circular top.
If the spider moves at a constant crawling speed, calculate the total length of the path to reach the ant at the quickest possible time. Please round-off your answer to the nearest four decimal places.
- It is understood there can be 2 possible positions, given a single y-offset. In this exercise please consider only the position as drawn above. That means at the top view, the ant and the spidert shall only be within the first and third quadrant, respectively.
- The dotted lines is not the spider's path. They are used only to project the heights to the side.
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