Tarzan swings down to save Jane

[dkgojackets]

Homework Statement

Tarzan (mass 98.3552) stands on a 4.45 m cliff next to a river. He grabs a vine of length 30.1 m whose point of support is directly above Jane (mass 57.5336). He grabs Jane at the bottom of his swing and has just enough speed to make it to the other side. How long does the rescue take?

Homework Equations

I assume some kinematics.

The Attempt at a Solution

I already solved the other two parts (Tarzans speed at bottom (9.339 m/s)and height of other side (1.7714 m). I triedd d = .5at^2 for both sides of the swing (down and back up) but didn't expect it to be right. It probably has something to do with harmonic motion?

 

[Ja4Coltrane]

I can see simple harmonic motion working here. divide it into two parts with separate values for omega (in the SHM, not omega of the rope). Not too hard to do for the first part because you know the final speed. set that equal to (omega)(amplitude) where amp is the max angle. For the second part, do it the same way, but first calculate the initial speed by using energy conservation. Can you go from there?

 

[Ja4Coltrane]

on second thought, I guess you already know that initial speed because you used momentum to find the height of the other side. That makes it easier.