1. (20 points) A hungry monkey is sitting on a tree branch, holding onto a vine. The vine is 10 meters long, perfectly straight, initially makes an angle of 60° with respect to vertical as shown, and can be treated as massless. The 10 kg monkey steps off the branch, and starts swinging down along a circular path. When he is at the lowest point of the swing, he grabs a 5 kg bag full of bananas, and he and the bananas continue swinging upward on the vine.
a.)How far past vertical (θ in the picture) do the monkey and bananas swing by the time they stop?
b.) At the moment just before the monkey grabs the bag,what is the tension in the vine? (assume the vine is perfectly vertical, since he is at the low point of the swing)