Answer:
[tex]T = 250.674\,N[/tex]
Explanation:
The vine experiments a centripetal acceleration while swinging (the stuntsman experiments a centrifugal acceleration), whose most critical point occurs at the bottom and can be described by the Newton's Laws:
[tex]\Sigma F = T - m\cdot g = -m\cdot \frac{v^{2}}{R}[/tex]
The minimum tension force that the vine must be able to support without breaking is:
[tex]T = m\cdot g - m\cdot \frac{v^{2}}{R}[/tex]
[tex]T = m\cdot \left(g-\frac{v^{2}}{R} \right)[/tex]
[tex]T = (82\,kg)\cdot \left[9.807\,\frac{m}{s^{2}}-\frac{\left(9\,\frac{m}{s} \right)^{2}}{12\,m} \right][/tex]
[tex]T = 250.674\,N[/tex]
