On a stormy night in 1760, the gunners at the Upper Benham Battery had drunk far too much ale and managed to mistake a boat entering Porthcressa bay for French invaders. Luckily, they were so inebriated that their shot was wildly off target and they were doubly fortunate that it didn't hit Hugh Town.
You will find the cache at the cannonball's landing point where an old crater can still just about be made out.
Use the firing information below to calculate the range of the cannon. If you remember your A-level physics classes you will have no problem; if not, you'll need to do some research. Next, you will need to go to the posted coordinates at Upper Benham Battery to find information that will give you the bearing along which the cannon was fired.
The acceleration due to gravity at St Mary's has been measured as "standard (Earth) gravity", g0. You may assume that the firing and landing altitudes were equal. Also, as luck would have it, the wind, air resistance and other forces all cancelled out so that the range turned out to equal the standard, parabolic theoretical value.
Once you have the range and bearing you have two options. If your GPSr has a sufficiently precise "project a bearing" function, you can use that to calculate the landing point. If not, you will need to do some trigonometry using the Ordnance Survey grid references (one under the cache page's headline coordinates and then load the puzzle solution and change the units on your GPSr to "British Grid"). The second method, that assumes a "flat Earth" geometry, was used for setting the puzzle and the methods may give slightly different answers.
In fact, it has come to my attention that this projection tool https://www.geocachingtoolbox.com/ gives an output about 100m south of the actual location. I suggest using the trigonometry and British Grid method.
The cannonball was fired with an initial speed of 145.40m/s at an angle of 30° to the horizontal.
To find the bearing, VWX.YZ° , along which the cannon was fired, look at the small plaque on the cannon. Taking a=1, b=2, ..., z=26:
V=2nd letter of the first word
W=1st letter of the first word minus 1st letter of the final word
X=2nd letter of the first word minus 2nd letter of the final word
Y=7th letter of the final word minus 2nd letter of the final word
Z=2nd letter of the final word plus 6th letter of the final word
There is a FTF pin as a reward. Congratulations to heartradio for claiming it.
Maintenance: One member or other of our extended family will be lucky enough to be staying on the islands for more than half of the year and will keep an eye on it.
Disclaimer: The story is not true, the gunners always acted professionally.