The Grey Labyrinth is a collection of puzzles, riddles, mind games, paradoxes and other intellectually challenging diversions. Related topics: puzzle games, logic puzzles, lateral thinking puzzles, philosophy, mind benders, brain teasers, word problems, conundrums, 3d puzzles, spatial reasoning, intelligence tests, mathematical diversions, paradoxes, physics problems, reasoning, math, science.


The Cannon

Long ago in Puzzlania, where intelligence is valued, wars are few, and all relevant information is stated in the problem, there was a war. Invaders tried to conquer the Puzzlanian people. Of course, they failed, but it was only through the bravery and applied cunning of the defenders.

During the war, along the border, a series of 100 meter high watch towers were erected for the purpose of defense. Atop each tower was a cannon and a guard.

Toward the end of the war, atop one of the towers, a guard waited impatiently for signs of the enemy. The enemy had been pushed well back, so the chances of him seeing any action were slim. So, like every Puzzlanian, he amused himself with thought puzzles. On this particular occasion, the puzzle he came up with was this:

The cannon was exactly level with the ground below him. When fired, a 10 kilogram steel ball would leave the cannon at two hundred meters per second (Puzzlanians made good cannons, which is another reason they won the war). What would happen, he wondered, if at the exact instant the cannon were fired, he dropped a cannon ball off the tower? Which ball would hit the ground first?

Assume that the cannon balls were of equal mass, air resistance and drag were negligible, and there were no important geographic features in front of the cannon like mountains, valleys, or other watch towers.

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