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This one is indeed just my fancy sprouted from a simple geometry problem.

Suppose on a Cartesian plane there is an object at $(0,1)$ moving in the horizontal positive direction at one unit distance per unit time. Meanwhile another object is at $(0,0)$ moving with the same speed but constantly heading towards the first object.

If the motion of the second object merits scrutiny, given that someone had looked into this problem before, what is the definition or name of the curve traced by the second object?

Parcly Taxel
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Jian Stanley
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  • is cycloid an example of what you're looking for? maybe i don't understand the question if not (not because you're not clear but because i didn't read the question so carefully lol) – BCLC Aug 15 '21 at 14:18

1 Answers1

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The chasing object follows a pursuit curve, and the exact scenario you describe (where the chased object has uniform velocity) is called a radiodrome.

Using equation $17$ in the second Wikipedia article and transforming coordinates so that the chaser starts at $(0,0)$ and the chased object starts at $(1,0)$ moving upwards, the chaser follows the curve $$y=\frac{x^2}4-\frac12(\ln(1-x)+x)$$

Parcly Taxel
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