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lamp23

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In plane-wind problems where you are given the velocity of the boat and the velocity of the wind, my textbook gave the solution as just adding the vectors. How do we know we can just add the vectors? Even though the wind might be blowing faster than my boat, won't my boat still make progress even if it's heading straight into the wind? What is being assumed in these problems about the masses or the forces that I'm missing?

Here is an example problem:

The problem: A plane leaves the airport on a bearing of 45 degrees traveling at 400mph. The Wind is blowing at a bearing of 135 degrees at a speed of 40mph. What is the actual velocity of the plane?

Here is an example problem:

The problem: A plane leaves the airport on a bearing of 45 degrees traveling at 400mph. The Wind is blowing at a bearing of 135 degrees at a speed of 40mph. What is the actual velocity of the plane?

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