Tarzan jumps from a cliff and grabs a vine. He jumps horizontally from the cliff with...

Tarzan jumps from a cliff and grabs a vine. He jumps horizontally from the cliff with initial velocity v₀ at the time t₀. The vine has mass M and length L. Initially, the vine is hanging straight down and is attached at its highest point, O. After the “collision” Tarzan remains attached to the 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 without friction to the point O. The moment of inertia of a rod around its center of mass is I = (1/12)ML². You can neglect air resistance.

(a) Find Tarzan’s velocity immediately before the collision with the vine (at t₁).

(b) What is the moment of inertia of the vine about the point O?

(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 the height?

Expert Solution

genius_generous answered 2 years ago

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