Solve Zenon's Paradox: Tips & Strategies

[mprm86]

How do you solve it?

 

[WORLD-HEN]

solve what?

 

[quasar987]

"Achille is 100m away from a turtle. He runs 10 times faster than the turtle. When he arrives at the point where the turtle was at the begining, the turtle will be 10m away from him. Then it will be 1m, 10cm, 1cm, ...farther. He will never meet up with the turlte."

The time elapsed between each "step" of the race is always smaller and smaller, and it doesn't add up to infinity. Instead, it converges towards the actual time when the runner meets the tortoise.

This time, which is finite, can be calculated using the equations of motion at constant (0) acceleration:

$$x_{achille}(t) = v_{achille}t$$
$$x_{turtle}(t) = 100 + v_{turtle}t$$

$$x_{Achille}(t) = x_{turtle}(t) \Leftrightarrow v_{achille}t = 100 + v_{turtle}t \Leftrightarrow t = \frac{100}{v_{achille} - v_{turtle}}$$