On problem set 1, can anyone explain supplemental problem 1A6 and how to approach it?

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- anonymous

On problem set 1, can anyone explain supplemental problem 1A6 and how to approach it?

- chestercat

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- phi

Do you mean the question that starts, "A small plane wishes to fly due north at 200 mph..."?

- anonymous

Yes

- phi

create a [N E] or [x y] vector to represent the plane's velocity
and do the same for the wind.

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- phi

For example, let the vector have components be i and j, as asked for in the question
+i will mean east, +j will mean north
(negative numbers will mean west or south)
using that definition , the velocity vector will have length 200 and direction north.
in other words, write plane= [ 0 200 ]
This will be the speed measured over ground

- phi

the wind is *from* the northeast, so it blows towards the southwest
this direction can be represented by a vector pointing to the left 1 unit and down 1 unit
[-1 -1]
make it "unit length" by dividing by its magnitude= \( \sqrt{(-1)^2 + (-1)^2}=\sqrt{2} \)
[-1 -1]/sqr(2)
now "scale" by 50 to make this vector the correct length
wind= (50/sqr(2) ) * [-1 -1]

- phi

Here is a graph showing what we want
|dw:1435697516276:dw|

- phi

The idea is the plane flies a bit to the east, and the wind blows it back on course.
The problem is to now find the i and j components of the "plane vector"

- phi

to solve for the "plane vector" P, given wind W, and Desired D
P + W = D
write it as
P= D-W
or
P= [ 0 200]- [ -50/sqr(2) -50/sqr(2) ]
subtract corresponding elements to get
P= [ 50/sqr(2) 200+50/sqr(2) ]

- phi

or about P= [ 35.36 235.36]
with speed 238 mph, and 8.5 degrees east of north

- phi

If this is not clear, see
https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/vectors/v/linear-algebra-vector-examples

- phi

and
https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/vectors/v/adding-vectors

- anonymous

Thank you so much!

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