Question

Problem Set 1, 1/A/6= where does the equation for w come from ? Why is there a -j and a sqrt(2) ?

Answer 1

https://www.khanacademy.org/math/precalculus/vectors-precalc/vector-basic/v/equivalent-vectors-examples

https://www.khanacademy.org/math/precalculus/vectors-precalc/vector-basic/v/example-finding-components-of-a-vector

Answer 2

There are many videos that will get you up to speed (too many!), but those two give a start.

the wind is coming from the northeast , which means it is moving in the direction 1 to the west (i..e -1 in the x or "i" direction) and 1 to the south (-1 in the y or "j" direction)
thus it has a direction <-1, -1>

the length of that vector is \( \sqrt{2} \)
see https://www.khanacademy.org/math/precalculus/vectors-precalc/magnitude-vectors/v/finding-vector-magnitude-from-components
if we divide that vector by its "length" we get a vector that has unit length (but the same direction:
< -1/ sqr(2) , -1/sqr(2) > or , factoring out the sqr:
<-1, -1> / sqr(2)

next, we "scale" this unit length vector to length 50 (to represent a speed of 50 mph):
50 * <-1, -1> / sqr(2)

Answer 3

to do this problem , you could sketch it out like this: