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

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phi
 one year ago
Best ResponseYou've already chosen the best response.0Do you mean the question that starts, "A small plane wishes to fly due north at 200 mph..."?

phi
 one year ago
Best ResponseYou've already chosen the best response.0create a [N E] or [x y] vector to represent the plane's velocity and do the same for the wind.

phi
 one year ago
Best ResponseYou've already chosen the best response.0For 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
 one year ago
Best ResponseYou've already chosen the best response.0the 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
 one year ago
Best ResponseYou've already chosen the best response.0Here is a graph showing what we want dw:1435697516276:dw

phi
 one year ago
Best ResponseYou've already chosen the best response.0The 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
 one year ago
Best ResponseYou've already chosen the best response.0to solve for the "plane vector" P, given wind W, and Desired D P + W = D write it as P= DW or P= [ 0 200] [ 50/sqr(2) 50/sqr(2) ] subtract corresponding elements to get P= [ 50/sqr(2) 200+50/sqr(2) ]

phi
 one year ago
Best ResponseYou've already chosen the best response.0or about P= [ 35.36 235.36] with speed 238 mph, and 8.5 degrees east of north

phi
 one year ago
Best ResponseYou've already chosen the best response.0If this is not clear, see https://www.khanacademy.org/math/linearalgebra/vectors_and_spaces/vectors/v/linearalgebravectorexamples

phi
 one year ago
Best ResponseYou've already chosen the best response.0and https://www.khanacademy.org/math/linearalgebra/vectors_and_spaces/vectors/v/addingvectors
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