Answer
The maximum speed that Tarzan could tolerate is 4.8 m/s.
Work Step by Step
At the bottom part of the swing, the maximum possible net force which could keep Tarzan moving in circular motion is:
$1150 ~N - (78 ~kg)(9.8 ~m/s^2) = 386 ~N$
With this maximum possible net force, we can find the maximum speed $v$.
$m\frac{v^2}{r} = 386 ~N$
$v = \sqrt{\frac{(386 ~N)(4.7 ~m)}{(78 ~kg)}}$
$v = 4.8 ~m/s$
Therefore, the maximum speed that Tarzan could tolerate is 4.8 m/s.