   Chapter 5, Problem 37P

Chapter
Section
Textbook Problem

Tarzan savings on a 30.0-m-long vine initially inclined at an angle of 37.0° with the vertical. What is his speed at the bottom of the swing (a) if he starts from rest? (b) If he pushes off with a speed of 4.00 m/s?

(a)

To determine
The speed of Tarzan at the bottom of the swing if he starts from the rest.

Explanation

Given Info:

The length of the vine is 30.0m .

Initial inclination of the vine is 37.0° .

The initial velocity of the Tarzan is zero

Define the zero of potential energy at the level of bottom of the arc.

Using the conservation of mechanical energy,

12mvf2+0=12mvi2+mgyi       (I)

The initial height of the Tarzan above zero potential energy is,

yi=l(1cosθ)       (II)

• l is the length of the vine
• θ is the initial inclination of the vine

On substituting equation (II) in (I) and re-arranging,

vf=vi2+2gl(1cosθ

(b)

To determine
The speed of Tarzan at the bottom of the swing if he pushes off with a speed of 4.0m/s .

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