Note: The above coordinates are NOT the location of the cache. The problem below will have to be solved to find the correct coordinates.
Warning: If you did not like high school level algebra and physics, then you may not enjoy doing this cache.
One day I was finishing a round of golf and noticed the moon in the sky. It was a couple hours before sunset, but the moon was very visible against the blue sky. My mind wandered a bit as I walked down the fairway and I thought to myself, “I wonder how far this shot I just hit would have gone if I could have hit it while on the moon… like Alan Shepard did.” Well, needless to say this gave me an idea for a geocache. What if someone with a swing like Tiger Woods, could hit a six-iron, the club that Alan Shepard used, from the surface of the moon, over the edge of a giant crater? How far would it go? How long would it be in flight? Hmmm... the possibilities.
I have come across quite a few different “puzzle” type caches, but have not yet come across one that required the use of some math AND science skills, so I thought that I would create one.
The solution to this problem does not take an engineering degree, or any rocket science to solve… just some high school level math and physics. (at least it was HS level, long ago when I was that age) If you don’t remember the equations that are needed you will be able to find them on the internet. However, beware… I have designed this so that you will actually have to do the calculations. If you try to use one of the “plug and play” type of solution calculators on the internet, you will most likely get the wrong answer(s). And I'm almost certain that you won't find one that will give you all of the needed answers. If you write out the formulas, and keep the units straight, you should get the correct answers. I chose the moon for this problem for several reasons - the gravitational acceleration is far less than on earth, moon has no atmosphere to produce drag, we've actually had an American hit a golf ball on the moon… and it makes it interesting. :-)
Here is the scenario: (reference diagram below)
A moon golfer hits a six-iron from near the edge of the crater Tycho - this is the crater that has the long ejecta rays that form a "star" pattern and can be seen with a pair of binoculars. As this is a "professional" moon golfer, the ball takes off at an initial velocity of 150 miles per hour (typical speed for a six-iron), and at an initial angle of 30 degrees (typical loft of a six-iron). You will need to find:
1)The final velocity of the ball (“Vf”) in miles per hour,
2)The horizontal distance it traveled (“x”) in miles,
3)The time the ball was in flight (“t”) in seconds,
4)and the angle it’s traveling when it lands (“a”) in degrees.
See figure below for further explanation.
The cache is located at:
N33.TT7DDD
W84.SSSAA7
(Note: the coordinates are in DecDeg format)
Where:
DDD = the horizontal distance traveled “x” in miles, multiplied by 100, minus 12 and then ‘rounded’ to the nearest whole number; ie. DDD = [(“x”miles)*100] - 12 rounded to integer.
TT = total flight time in seconds (t) minus 20, and rounded to nearest whole number; i.e., TT = (“t” sec) - 20, rounded to nearest integer.
AA = the final approach angle “a”, in degrees minus 20, rounded to the nearest whole number. i.e., AA = ("a" deg.) - 20 rounded to the nearest integer.
SSS = the final speed “Vf” in miles per hour minus 37; ie SSS = ("Vf" mph) - 37, rounded to nearest integer.
Here is the only information that you will need to get the above answers: (You should use at least three significant figures after the decimal point for all your calculations to avoid rounding discrepancies.)
• Mass of moon = 7.349 x 10E22 kg (from NASA)
• Radius of moon = 1.738 x 10E6 meters
• Gravitational constant “G” = 6.67428 x 10E-11 m3/kg*s^2 (from NIST)
• Depth of Tycho crater = 4.80km = 4,800m
• Initial velocity = 150mph
• Initial angle of flight = 30deg
(Note: there are different sources of values for each of the above constants. The ones given are from NASA and NIST, so use the values above, or you may get different answers.)
The cache is a regular size (2+ liters) camouflaged container, with a water-tight screw on lid. It has a logbook, pens, golf balls, and playing cards. Please seal the container and return it to its proper configuration. Do NOT approach this cache from private property located to its NW or N. The cache may be approached from the SE, S, or SW without trespassing.
You can check your answers for this puzzle on Geochecker.com.
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