The aliens are hovering their UFO over Boji Tower (N 42 43.969, W 84 33.218), the tallest building in Lansing. Their laser is firing from a height of exactly 484.8 meters.
Their laser strikes a mirror which their spies have covertly mounted on top of Beaumont Tower (N 42 43.919, W 84 28.929), home of a beautiful 49 bell carillon. You should really go hear it some time. The mirror is at a height of exactly 34 meters. The mirror starts each hour aligned exactly north to south (like a minute hand at 12:00, if north is up), and rotates in a clockwise direction. It makes one rotation per hour.
Our poor little escaped Cap-cap is hiding behind a tall object. However, at precisely 3:15:46 PM, the laser illuminated that object at a height of 3 meters. The resulting glow gave away her position. A small adjustment to the laser and... it's all too tragic.
Update: As the original container has been muggled, the new cache is not a cap-cap, but a traditional keybox. It is no longer at the the base of the tall object, but is now about a foot or two to the west. Should be fairly obvious where to look, and still within the margin of error for the original coordinates.
To find the Cap-Cap, assume a spherical earth of radius 6378 kilometers.
Update: IFollowRoads sent me a fascinating message with a number of ways I could have made this puzzle even harder. Here's a list of things you DON'T have to worry about:
- You may neglect the earth's curvature, except for purposes of converting longitude to distance.
- You may assume the mirror is mounted so that the axis of rotation is VERTICAL.
- You may assume the mirror is reflective on both sides.
- You may assume the mirror is infinitely thin, and perfectly reflective.
- You do not need to worry about any structures between the UFO, Beaumont Tower, and the cache.
- You may assume the motor's motion is smoothly continuous, to any degree of precision desired.
- You may assume the "sea level" from which all the altitudes are given is precisely equivalent.
This cache was inspired by GC142C8, "Leipziger Fernsehturm." Be happy YOU don't have to solve this in a foreign language, unless you are a German tourist. It is part of the Cap-Cap Invasion! series.
