*** The cache is NOT at the posted coordinates ***
Where does the cue ball stop?
A Geocacher freak decided to use a custom-made cloth for his pool table. He decided to use an aerial map view similar to the picture below:
He then decided that it would be a really cool idea to hit the cue ball with the cue stick and hide a cache wherever the cue ball stops and see if other geocachers can find his cache. NOTE: The image above does not necessarily represents the image to be used in puzzle pool table.
Puzzle:
A= N 42° 40.170 W 083° 03.126
B= N 42° 40.170 W 082° 53.126
C= N 42° 35.170 W 083° 03.126
D= N 42° 35.170 W 082° 53.126
Tournament pool dimensions: 100 inches x 50 inches.
Cue ball diameter = 2.25 inches.
Cue ball initial velocity = 370 inches per second @ 30° as shown in the diagram.
Cue ball constant decceleration from cloth fiction = 420 inches per squared seconds.
Cue ball initial position is at half the width of the table and 15 inches in front of the left edge as show in the diagram below.
Cue stick angle at 30° as shown in the diagram below.
For puzzle simplicity we are going to make the following assumptions: Pool table has no holes as shown in the diagram. Constant cloth friction decceleration. No energy loss when the ball hits the edge bumpers (No loss in velocity when the ball hits the edge bumpers). When the ball hits the edge at an angle, the exit angle is going to be the same but in the opposite direction. No spinning or other trick shot effects. No air resistance losses.
Cache location is where the cue ball stops.
FTF will get a Kart Race; 2TF will get a laugh (at a comedy club)
Congratulations Paddling Pirates on a well done FTF after traveling 70 miles each way!!!
You can check your answers for this puzzle on Geochecker.com.