Tarzan tries to cross a river by swinging from one bank to the other on a vine that is 12.2 m long. His speed at the bottom of the swing is 8.6 m/s. Tarzan does not know that the vine has a breaking strength of 1.0 * 10^3 N. What is the largest mass that Tarzan can have and still make it safely across the river?

The point where the tension in the vine is highest is when Tarzan is at the lowest point. Find the centripetal force required, find the weight of Tarzan and find the resultant force, using:

Tension = Centripetal Force + Weight

Then find the force that Tarzan can still carry (if he can).