Answer
(a) Tarzan's acceleration is not zero. Tarzan is in free-fall so his acceleration is $g$ and this acceleration is directed straight down toward the ground.
(b) Tarzan's acceleration is not zero. Tarzan's acceleration points straight up.
Work Step by Step
(a) Immediately after stepping off the branch, Tarzan's acceleration is not zero. Tarzan is in free-fall so his acceleration is $g$ and this acceleration is directed straight down toward the ground.
(b) At the lowest point in Tarzan's swing, there are two forces acting on Tarzan. The tension force from the vine points straight up and the force of gravity points straight down. Since the tension is greater than Tarzan's weight, the net force is directed straight up. Therefore, Tarzan's acceleration also points straight up.
