Jane, looking for Tarzan, is running at top speed (5.0 m/s) and grabs a vine hanging vertically from a tall tree in the jungle. How high can she swing upward? Does the length of the vine affect your answer?

VIDEO TRANSCRIPT

This is Giancoli Answers with Mr. Dychko. The total energy, after the Tarzan gets to the full height, is equal to the total energy that Tarzan had before he grabbed on to the vine. So total energy, in the final case, is equal to the potential energy because the speed will be zero at the top of the swing, so it's mgh. And initially, there's no potential energy because the ground that he is running along is the reference level, so that's zero. And initially, he has only one-half m v i squared kinetic energy; and we can solve for h by dividing both sides by g after canceling the m's and we get the maximum height it could reach is v initial squared divided by 2 g. So that's 5 meters per second squared divided by 2 divided by 9.8 meters per second squared which gives 1.3 meters as the maximum height. And the length of the vine does not matter, provided the vine's at least 1.3 meters long, so that Tarzan can reach that maximum height. You can see two pictures here, where the vine is longer than 1.3 meters, and the thing that changes is the angle; with a long vine, you get a small angle; with a short vine, you get a big angle; but that doesn't really matter, you still get the same change in height of 1.3 meters, which is the only thing that matters as far as energy is concerned.