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

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1. phi

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

2. anonymous

Yes

3. phi

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

4. 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

5. 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]

6. phi

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

7. 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"

8. 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) ]

9. phi

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

10. phi
11. phi
12. anonymous

Thank you so much!