The Physics of an Elephant-Powered Slam Dunk

From the coefficient on the x2 term, –0.1816, I can find the initial velocity v0 (assuming this elephant jump takes place on Earth, with a gravitational field of g = 9.8 N/kg, which seems like a safe bet).

Illustration: Rhett Allain

If you don’t have a good feel for velocities in meters per second, that’s about 20 mph. That’s a nice and reasonable speed. OK. I’m pretty satisfied. I think this is a real video. Although this makes me a little worried about this guy. If he thinks jumping over two elephants is a good idea, what other crazy-dangerous stuff will he try?

Now for some more homework questions. I’ll give you some hints, but I’m giving you a chance to answer these before I come back to them in the future.

  1. What are the acceleration and force during the launch?

Ignoring what happens later, the launch itself could be dangerous too. A giant animal is exerting a significant force on a puny human through the board. Can you estimate the force that the board exerts on the guy during the launch? Also, find the acceleration during the launch phase (so you won’t need to know the exact mass of the dude). It will be useful to find the acceleration in units of g’s, where 1 g = 9.8 m/s2. So you know, a human can withstand around 20 g’s without serious injury. My guess is that this movement is less than 20 g’s.

One hint: During the launch motion, he moves just under 2 meters. It’s probably better to use distance rather than time when calculating the (average) force and acceleration.

  1. What are the acceleration and force on the landing?

This is basically the same question, but on the other end. So, how about a twist? What if he landed only on the bale of hay? What would his landing acceleration be if his center of mass moved 60 centimeters during the landing phase? This distance would include the motion of his legs bending and the compression of the hay. Of course, in the video, the hay doesn’t fully stop him, but instead just slows him down a little. That’s a smart move.

  1. Estimate the elephant power.

When the elephant pushes down on the launching board, find the power input. You might want to calculate the force from the elephant pushing down (that’s optional). But even without that, you can still calculate the power. Trust me. Oh, what is the power of an elephant in horsepower, where 1 hp = 746 watts? Yes, the only reason for this question is to set up elephant power as a unit of power.

  1. Correct for the slow-motion segment.

Clearly the middle of the video is in slow motion. This means the playback frame rate is not the same as the real time in between frames. So, what is the playback speed for this video? Let me give a quick example so you understand what’s going on here. Suppose the normal playback rate is 30 frames per second. If this was in slow motion at half speed, it would play at 15 fps—but each frame would still represent 1/30th of a second in real time.

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