Early one Saturday morning we set out to sail in our hot air balloon on a journey which would take us from Leavenworth, Wa to Moses Lake, WA, nearly 90 miles away. However, for our geocaching friends, we dropped a cache from the balloon while sailing over Wenatchee, WA. (I brought along my GPS so we could chart our journey). At 5:15 AM we headed over to the Safeway parking lot in Leavenworth (Site 1), where we were given prior permission to launch. The coordinates for the point of lift off is N47 36.000 and W120 38.820. When we arrived we were just in time to see the balloon being inflated. The balloon company we had hired for this excursion were very efficient and had the balloon ready for lift off in no time. Even in the dimness of the just breaking light the multicolored fabric took on a brilliance as it rose to its towering height.
Finally, our balloon was ready and at 5:40 AM, after the ground crew released the tie downs, we floated away, just clearing the tree tops. The wind speed was measured to be 8 mph and the direction was perfect for taking us in the direction we wanted to go. It grew light enough for us to see a herd of elk in the forest below us and later we saw a few deer. The early morning light turned the Wenatchee River into a silvery mirror. The pilot continued elevating the balloon higher and higher by heating the air inside the balloon with the propane burner, until at 6:30 AM we were at an elevation of 5000 feet. Our location was 6.868 miles (11.053 km) and 124.68 degrees True from the starting point (Point 1) in Leavenworth.
At that point we were directly over The Peshastin Pinnacles (Site 2), a series of sandstone slabs and spires. The climbable spires reach 200 feet into the air giving climbers views of surrounding orchards, the Enchantment Mountain Range, and the Wenatchee River Valley. Because of the elevation and the proximity to the foothills, the wind shifted immediately and picked up speed. We were now heading in a southeasterly direction, however we were still on course toward Wenatchee. We were now traveling at 127.44 degrees True. For most of the journey we were heading over orchard country, and following the Wenatchee River as it meanders through the valley toward Wenatchee. The apple trees below were whitened with blossoms. To the northwest, we could see 10,541 foot Glacier Peak.
After a while, we were just over the small town of Monitor, WA, (Site 3). Then the wind changed direction once more. I noticed from my GPS we were 6.3666 miles (10.246 km) from the Pinnacles (Site 2). The wind direction was now 82.75 degrees True. We stayed on this course and after several minutes we found ourselves approaching the town of Wenatchee. We got ready to drop the cache. We looked down and made sure we weren’t going to drop it in a residential or commercial area. We just passed Birch Mountain when we found a good area, we dropped the cache and watched it plummet toward earth (Site 4), and found the distance from Site 3 to be 4.0364 miles (6.496 km). It was just after 8:00 AM and we then proceeded on our journey and headed on to our final destination of Moses Lake, WA. Our chase crew kept an eye on us during the entire trip and eventually met us at the the rendesvouz site and assisted in a safe landing.
From the information given above, solve for the cache coordinates, and locate the cache.
For purposes of this exercise, the following criteria are allowed:
Assume the cache falls vertically toward earth from the point it is released. Assume also that change in direction of the balloon is instant.
This Bearing/Distance Calculator is a nice tool for figuring out the waypoints. Be sure to use the Spherical Method. Hint: This site uses kilometers for distance, which is provided in the story problem. You'll also have to change the coordinate format from Degrees Decimal Minutes to Degrees Minutes Seconds. (You're GPS may have this function. If not go to JeEep.com Coordinate Translation). Just enter Site 1 coordinates and leave Site 2 blank. Also enter the distance (kilometers) and the bearing. Click "Compute" for the second waypoint. Repeat this 2 more times until you get the final cache coordinates.
Good luck. The Navigatorz
NOTE: In case you were wondering, this above story is only fiction. We didn't drop the cache from a balloon. It was placed by hand. 