Question

A 58kg boy runs at 6.5m/s grabs a hanging 10m long rope and swings out over the lake. He releases the rope when his velocity is zero.
a.What is the maximum tension in the rope during the swing?

Answer 1

$$T\cos{\theta}=mg$$

$$0.5mv^2=mgl(1-\cos{\theta})\to v^2=2gl\left(1-\frac{mg}{T}\right)$$

$$6.5^2=2(9.8)(10)\left(1-\frac{(58)(9.8)}{T}\right)$$

$$T=725\ N$$