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November 01, 2025, 03:08:57 pm
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Author Topic: A vectors question~  (Read 1035 times)  Share 

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tryingtobeoptimistic

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A vectors question~
« on: January 25, 2011, 06:48:08 pm »
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Can anyone help me with this question? ???

A small plane can fly at 82m/s in still air. There is a wind of 5i +18j m/s. What course should the pilot set, and how long will it take him to fly 51km due east?

Thanks  :)
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schnappy

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Re: A vectors question~
« Reply #1 on: January 25, 2011, 07:53:04 pm »
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Not long.
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tryingtobeoptimistic

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Re: A vectors question~
« Reply #2 on: January 25, 2011, 08:03:37 pm »
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Quote from: schnappy on January 25, 2011, 07:53:04 pm
Not long.
haha. I know its 10 mins but not sure how to solve it   :o
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kamil9876

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Re: A vectors question~
« Reply #3 on: January 25, 2011, 10:00:03 pm »
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Weird, but anyhow I'll assume "course set" means that the direction the pilot is applying thrust, and that the wind velocity "adds" to the velocity given by the plane. (weird assumptions but oh well).

Then suppose the guy applies a velocity of

Then we know that his actual velocity is the vector sum:



Hence you need so that he moves east.

you also have the constraint:


solving gives (taking positive solution as we want to move east). So you know he must "set his course" in a direction of

Now the time taken is
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Voltaire: "There is an astonishing imagination even in the science of mathematics ... We repeat, there is far more imagination in the head of Archimedes than in that of Homer."
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