Tarzan tries to swing across a river on a 12.0 vine. His speed at the bottom of his swing is 10.5 m/s. The vine has a breaking strength of 1.73x10^3 N. What is the largest mass Tarzan can still have? Thanks in advance.

Do you realise that you're dealing with centripetal forces? I'll give you a hint; the tension in the vine will be given by the sum of tarzan's weight and the centripetal force.

You can use

F_c=\frac{mv^2}{r}

where F_c is the centripetal force, m is the mass of Tarzan, v is his speed and r is the radius of the pathway.