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Track a Tank Shell With a Mirror and Polar Coordinates

Condé Nast

The Slow Mo Guys


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The New York Times
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It's possible to use the position to calculate the angle to aim the mirror—but that's not as much fun as using polar coordinates.Oh, I should also point out that if you move the origin of the Cartesian coordinate system it's not a big deal. Sure, you will have different starting positions, but the velocity equations mostly look the same.If you are still dealing with motion on a flat plane (ignoring the vertical motion of the tank shell), you will need two coordinates to describe the location of the object relative to the origin. Instead of using two perpendicular distances (x and y), polar coordinates uses an angle and a distance. Here is the same object from before using polar coordinates.Instead of x and y, we use r (the distance from the original) and θ the angle from the x-axis. Why would anyone use polar coordinates? Because with polar coordinates, you get the angular position of the object. Oh, notice that if I move the origin for the polar coordinate system the values can change quite a bit.OK, let's just do this.

As said here by Rhett Allain