A massless rope hangs vertically from a tree. A child runs toward the

Question

rope at speed 5m/s and grabs the end of the rope. This causes the child
to lift off of the ground, swing up into the air, and then to come back
down. The total time that the child is off the ground is 5sec. Treat the
child as a point mass of zero size and all angles as small.
(a) What is the length of the rope?
(b) What is the child’s maximum height off the ground during their swing?