Ok, here we go. This is my first post on this forum, and its a fun one. I have a problem that is pretty dang hard. I have spent a lot of time thinking about it, but i have yet to come up with anything. Read the problem carefully because there are no numbers involved. Ok, here it is.

Ok, so there is a pond. The pond is a perfect circle and the radius of the circle/pond does not matter. In the middle of this pond there is a fish. The fish wants to escape the circle. However, at the edge of the circle there is a shark. The Shark CAN ONLY move on the outside of the circle. The fish, can move in any direction it wants to. The shark is trying to prevent the fish from escaping the circle. Both the shark and the fish move at constant speeds and can change direction instantly.

Ok, so here is what we are supposed to find. We have to find How many times faster does the shark have to swim (the shark swims x times faster than the fish) IN ORDER TO PREVENT the fish from escaping the circle.

The person who gave us this problem said you must use calculus to solve this problem. If the fish decides to swim in a straight line, then the shark has to swim Pi times faster than the fish. However, the fish is not dumb, it will try to move in a more complicated path than just a straight line. So we know the answer has to be greater than Pi.

The first step of the problem is finding the ideal path for the fish to swim. The second step is finding an equation to model this path. And the third step is probably to integrate that equation. (im guessing).

Sorry if this is a little long but I have to be sure to explain it. Have fun trying the problem but i will understand if you don't even want to try it at all XD. I know that there are some smart people on this forum so hopefully this problem can be a fun challenge for them