Off to find Jane
Tarzan is often portrayed as swinging through the jungle from vine to vine. Each of Tarzan's vines are 30 meters long and Tarzan catches each vine when it is at rest 15 degrees to the left of the (downwards) vertical, swings on it until it stops at an angle of 15 degrees to the right of vertical, and then grabs the next vine at rest and repeats the process.
What is Tarzan's average horizontal speed in m/s ?
Details and assumptions
- You may take g to be .
- You may treat Tarzan as a simple pendulum and use the small angle approximation.
The answer is 2.82.
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1 solution
Tarzan on the vines in the small angle approximation is a simple pendulum. The period of a pendulum T is
T = 2 π g L .
Tarzan only goes half a period on each swing (he doesn't swing back) so the time for one swing is T = 5 . 5 s . The horizontal distance traveled in one swing is 2 × 3 0 × sin 1 5 ∘ = 1 5 . 5 3 m , and so his average speed is v = 1 5 . 5 3 / 5 . 5 = 2 . 8 2 m/s .