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Great Stunt, Spider-Man! Now Let’s Fine-Tune the Physics


Here, g is the gravitational field, with a value of about 9.8 newtons per kilogram. If you’ve ever taken a physics class, you’ve heard that number so many times you still mutter it in your sleep. The gravitational field weakens as you move away from Earth’s surface, but so long as you don’t jump a hundred miles into the sky, we can treat it as a constant.

Gravity’s rainbow

So what does a force do to an object? It makes it accelerate. For gravity, that means a falling object will pick up speed as it plummets to Earth. (This is why it’s unwise to jump off tall buildings.) To be specific, it accelerates downward at a rate of 9.8 meters per second per second (m/s2).

Instead of jumping down, what if you jump up and forward onto a plat­form? The physics don’t care. You launch with a certain velocity, which we can break into horizontal and vertical components. The horizontal velocity, per Newton, never changes. But gravity immediately starts winding down the vertical part: Your rise slows until it becomes negative—i.e., downward—velocity, and then you fall faster and faster until the platform (or the ground) stops you.

And here’s the key point: It doesn’t matter if you’re an ordinary mortal or a superhero; the vertical acceleration is the same –9.8 m/s2. With superhuman leg strength, you get a better push-off, so your initial velocity is higher and it takes longer for gravity to turn you around. That means you can jump higher. But the effect of gravity should look the same.

Now, if we put this vertical acceleration together with the fixed horizontal velocity, we get something special, called projectile motion. You know it as the beautiful arching, parabolic path of a ball tossed across a room, or a cup of coffee knocked off a table, or any hapless thing launched into the air.

This is great, because it means that even the real Spider-Man would move in a way governed by introductory physics. So now I can measure Tom Holland’s vertical acceleration and compare it to what it would be without a harness—that is, if it were true projectile motion. That basically deter­mines how convincing the illusion looks.

Supermen are from Mars?

First, I’m going to plot the actor’s spatial coordinates in each frame of the video using the free and awesome Tracker video analysis tool. Then I’ll try to fit a quadratic equation to the data. Why quadratic you ask? Because if you graph a quadra­tic equation, you get a parabola!

For an object with constant vertical acceleration, the following formula describes its height (y) as a function of time (t). We call this a kinematic equation. y0 is the starting height, vy0 is the initial velocity, and a is the acceleration.

Rhett Allain

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