Achilles gives a tortoise a 100-meter head start. Achilles runs at 10 m/s, the tortoise at 1 m/s. Zeno argues Achilles can never catch the tortoise because he must first reach where the tortoise was, but by then the tortoise has moved. (1) Resolve the paradox using limits. (2) Resolve it without calculus — using only physical reasoning. (3) Is there a version of Zeno's paradox that modern physics cannot fully resolve? (Hint: consider Planck length.)