Hey there Physics friends!
I've been struggling with what seems to be a very basic physics question. Let's say that I have wind vector for a given altitude and location, and I want to calculate the flight path of a hot air balloon.
So once the balloon hits that wind, would you calculate forward distance based on the wind speed (so would the balloon speed be exactly the average wind speed) or would you use the standard drag equation to calculate the force of the wind on the balloon to determine the distance traveled by the balloon in a given time period?
Answer
Yes you would have to use the standard drag equation. Imagine the balloon is at rest (or moving with a different velocity from the wind) initially. As the balloon hits the wind it can't suddenly reach the same velocity as the balloon, as this would require an infinite acceleration (which is impossible). Instead the wind applies a force to the balloon. This force will increase the balloon's velocity until it does match that of the wind (drag force is proportional to the relative speed between the balloons), at which point the velocity of the balloon will match that of the wind. If you can assume that the time it takes for the balloon to reach the velocity of the wind is negligible (such as in the case of a large drag coefficient or cross sectional area of the balloon) then the velocity of the balloon could be assumed to be the same as that of the wind at all times.
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