Tarzan jumps from a cliff and grabs a vine. He jumpshorizontally from the cliff with initial velocity v0 atthe time t0. The vine has mass M and length L.Initially, the vine is hanging straight down and is attached at itshighest point, O. After the “collision†Tarzan remains attached tothe vine with his center of mass at the lower edge of the vine.Tarzan’s mass is m. The vine behaves as a rod attached withoutfriction to the point O. The moment of inertia of a rod around itscenter of mass is I = (1/12)ML2. You can neglect airresistance.
(a) Find Tarzan’s velocity immediately before the collision withthe vine (at t1).
(b) What is the moment of inertia of the vine about the pointO?
(c) Show that the angular velocity of the vine (with Tarzan)immediately after the collision is ω2 = m/((M/3) +m)(v0/L).
(d) How far up does Tarzan swing?
(e) How high would Tarzan swing if he jumped from twice theheight?
