1. ## Projections

Okay, I have a test in a few days and I feel like I'm getting stuck on easy questions but I never did get a proper example shown to me so I'm not quite there yet.

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A boat heads across a river at a rate of 4 miles per hour. If the current is flowing east at a rate of 3 miles per hour, find the resultant velocity of the boat. Also find the projection of v onto u.

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Now I understand c^2 = a^2 + b^2
= 3^2 + 4^2
c = 5

5 miles per hour. I get that. How do I do the projection of v onto u?

projec u V = ( (u)(v) / U^2 ) (u)

u = ?
v = ? How do I get them when there is a 0 involved?

The text says the answer is 5 m/h at an angle of 53.13 degrees to the bank.

How?

2. I know how to do this with basic trig: cah cos = a / h = 3 /5 cost -1 (3/5) = 53.13

How do I do this with linear algebra and show my steps using the proper formulas?

cost feta = ( vec(u) dot (vec v) ) / ((length of vec v)(length vec u))

or proj u V = (((vec u)(vec u) / (vec u)^2 )(vec u)

I guess I need to figure out how to do get vec u and vec v to use in the formulas.

3. How are u and v defined in the problem statement?

4. NM, the stupid textbook had an error. Projections not needed on this question. Of course the error was a "make a projection of V onto u for the next 5 questions" which made it weird to follow the instructions.

Oh well.

5. Well, so long as you're all set.