A hot air balloon competition requires a balloonist to drop a ribbon onto a target on the ground. Initially the hot air balloon is 50 meters above the ground and 100 meters from the target. The wind is blowing the balloon at v = 15 meters/sec on a course to travel directly over the target. The ribbon is heavy enough that any effects of the air slowing the vertical velocity of the ribbon are negligible. How long should the balloonist wait to drop the ribbon so that it will hit the target?
Assuming the ribbon falls fast enough to hit the ground before it overshoots the target, from 100 meters away in a wind blowing 15 m/s it would take 100/15 = 6.67 seconds for the ribbon to be over the target. However, it will take only 3.194 seconds for the ribbon to hit the ground no matter when it is dropped. So, the balloonist needs to wait until it takes 3.194 seconds before the balloon is over the target. At 15 m/s the distance covered will be 15 x 3.194 = 47.91 meters. Since the balloonist is 100 meters away, he or she needs to wait until this distance is reduced to 47.91 meters, or wait until the balloon has moved 100 – 47.91 = 52.08 meters. At 15 m/s this will only take 3.47 seconds.
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Alex & the 1936 RCA 44 B Ribbon Velocity Microphone
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