Tarzan's velocity while swinging on his vine

[smileyjen523]

Tarzan swings on a 40m long vine intially inclined at an angle of 40 degrees with the vertical. Acceleration of gravity = 9.81 m/s^2. What is his speed at the bottom of the swing if he starts from rest?

i started by drawing a diagram. and then i used trig to find the distance between the intial position and the bottom of the path. then i tried to plug that into a kinematics equation i think, but it didn't work. i used something like Vf^2=Vi^2+ad

help would be great appreciated. thanks.

 

[gdumont]

Use energy conservation : At time $t=0$ Tarzan has zero kinetic energy (he is at rest).

If Tarzan is, say, $l$ meters above the ground, can you find an expression for his potential energy? Then you can relate $l$ with the length of the vine using trig.

Then at the bottom of the swing all energy is converted to kinetic energy. You can easily find an expression for that too.

By equating both energies you'll be able to find the speed of Tarzan at the botton of his swing.

Hope this helps!