GeekDad Puzzle of the Week Answer: That Darn Achilles

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Sean S.'s awesome contribution to projectile motion: "Wow, projectile motion, I haven't done this since high school; this is great!"

This week’s puzzle asked how to shoot an arrow as far as possible from the walls of Troy. Ah yeah, projectile motion, baby! (Or as Laurion wrote, “Oooh, trajectory calculations!” Thank you, Laurion….me too!) And if you ever took physics 101, you know that in the absence of a constant, you can disregard wind resistance (not really — but so go physics 101 problems). Here was this week’s question:

You, Paris, have the luxury of launching an arrow at faraway Achilles either from the ramparts above the Hesperian Gate at a height of exactly 8 meters. Or you can stand atop Priam’s palace. This gains you another 7 meters of launch height, but it costs you 15 meters of horizontal distance. If the arrow leaves your bow at a somewhat modest 70 meters per second, are you best taking your pot-shot at far-off Achilles from the ramparts or the palace? Which perch offers the farthest reach?

As you may have noticed, this is a plug-and-play equation. And despite that, solutions were far ranging (no pun intended) and diverse. Some people assumed we were shooting horizontally — no, we should probably assume that while Homer portrayed Paris as a limp-wristed, wet towel, nonetheless he knows how to maximize the distance of an arrow.

The winner this week, randomly chosen from correct entrants, in Christopher, who wrote, “From years of playing cannon battle on the Apple ][, I ‘know’ that the ideal angle for greatest distance is 45 degrees, but I’m not ready to stipulate that immediately.”

It’s good when the week’s answer also happens to be awesome. And the answer is that Paris will get better distance from the ramparts, from which the arrow travels 508 m, as opposed to 500 m from the palace.

Congrats, Christopher on your $50 ThinkGeek gift certificate! The rest of us can use code GEEKDAD59MJ to get $10 off a $50 order.

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