Question

Tarzan, in one tree, sights Jane in another tree. He grabs

theend of a vine with length 20 m that makes an angle of 45
degreeswith the vertical, steps off his tree limb, and swings down
andthen up to Jane's open arms. When he arrives, his vine makesan
angle of 30 degrees with the vertical. determine whetherhe gives
her a tender embrace or knocks her off her limb bycalculating
Tarzan's speed just before he reaches Jane. Youcan ignore air
resistace and the mass of the vine.

Answer 1

He knocks her. V = 7.97m/s

Step-by-step explanation:

Let A be Tarzan's starting position and B Jane's position (Tarzan's final position).

Since there is no air resistance, energy at position A must be equal to energy at B.

At position A, Tarzan's speed is zero and since the 45° of the vine is greater than the final 30°, Tarzan will have potential energy at point A.

`E_(A)=m_(T)*g*L*(cos(30)-cos(45))`

At point B, it is the lowest point (between A and B), so it has no potential energy. It will only have kinetic energy (ideally zero, for Jane's sake, but we don't know).

`E_(B)=(m_(T)*V^(2))/(2)`

Because of energy conservation, we know that Ea=Eb, so:

`m_(T)*g*L*(cos(30)-cos(45))=(m_(T)*V^(2))/(2)` Solving for V:

`V=√(2*g*L*(cos(30)-cos(45)))=7.97m/s`