Skip to Content
Uncategorized

The Counterintuitive Physics of Tarzan Swings

When Tarzan leaps from a swinging rope, when should he let go to jump furthest? The answer isn’t as simple as you might think

Let’s ignore air resistance for a second. If you point a cannon, aim an arrow or throw a basketball, the trajectory that gets you furthest will be at 45 degrees to the vertical. So the same must be true for Tarzan on a rope swing. He ought to let go when the rope is at 45 degrees to the vertical, right?

Not so, says Hiroyuki Shima at the University of Yamanashi in Japan, who today takes us through some straightforward calculations to show the answer is not quite as intuitive as you might imagine. 

Shima begins by defining the question as in the diagram above. The problem, of course, is that Tarzan’s horizontal velocity reaches a maximum when the rope is at the bottom of its swing, at 0 degrees to the vertical. 

By hanging on beyond this point, Tarzan begins to convert some of this horizontal velocity into vertical speed, which sends him on an upwards parabolic trajectory that can increase his time in the air and therefore the distance he travels along the ground .

The balance that has to be struck is between the lost horizontal velocity and the vertical velocity gained. When does this maximise the horizontal distance he travels?

Shima shows first that to maximise the distance, the angle of the rope at the point of release should always be less than 45 degrees. That’s in stark contrast to the case of throwing or firing a missile, which is why this problem is a little counterintuitive.

He goes on to show that Tarzan cannot significantly increase his flight duration by hanging on to the rope much beyond the lowest point  of the swing. “The flight duration is not significantly altered by acquiring the upward component,” he says.

So a small angle of release is ideal, although not too small an angle. 

In fact there is no simple rule for maximising the horizontal flight distance. It turns out this depends on a number of factors, such as rope swing’s distance off the ground, the length of the rope and the angle of the rope when Tarzan begins his swing as well as the angle of the rope at the point of release.

So there you have it: a well posed problem with some interesting physics to boot. Johnny Weissmuller would be pleased. 

Or as he would put it: Aaaaaaaaaayaaahh-eeeeeeeeeeeeyaaaaaaah-aaaaaaaaaaaaaaaaahaaah.

Ref: arxiv.org/abs/1208.4355: How Far Can Tarzan Jump?

Keep Reading

Most Popular

Large language models can do jaw-dropping things. But nobody knows exactly why.

And that's a problem. Figuring it out is one of the biggest scientific puzzles of our time and a crucial step towards controlling more powerful future models.

OpenAI teases an amazing new generative video model called Sora

The firm is sharing Sora with a small group of safety testers but the rest of us will have to wait to learn more.

Google’s Gemini is now in everything. Here’s how you can try it out.

Gmail, Docs, and more will now come with Gemini baked in. But Europeans will have to wait before they can download the app.

This baby with a head camera helped teach an AI how kids learn language

A neural network trained on the experiences of a single young child managed to learn one of the core components of language: how to match words to the objects they represent.

Stay connected

Illustration by Rose Wong

Get the latest updates from
MIT Technology Review

Discover special offers, top stories, upcoming events, and more.

Thank you for submitting your email!

Explore more newsletters

It looks like something went wrong.

We’re having trouble saving your preferences. Try refreshing this page and updating them one more time. If you continue to get this message, reach out to us at customer-service@technologyreview.com with a list of newsletters you’d like to receive.