Question

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

Answer 1

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

Answer 2

Yes

Answer 3

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

Answer 4

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

Answer 5

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]

Answer 6

Here is a graph showing what we want