# Relative Vectors Problem

1. Aug 24, 2011

### dGasim

1. The problem statement, all variables and given/known data
A woman walks due west on the deck of a ship at 3 mi/h. The ship is moving north at a speed of 23 mi/h. Find the speed and direction of the woman relative to the surface of the water. (Round your answers to one decimal place.)

2. Relevant equations

3. The attempt at a solution
First I drew the picture:
EDIT: Attachment

Then I solved the relative velocity formula:
$v_{w/g} = v_{s/g} + v_{w/s}$ = 23 + 3 = 26mi/h

Which went wrong, so I made another attempt:
$\sqrt{23^2 + 3^2} = 23.2$

And i don't know how to find the angle. Should I do it like arctan(23/3) ?

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2. Aug 24, 2011

### tiny-tim

Hi Gasim!
Your formula is correct , but of course it's a vector formula, so you must always use vector addition (so your second try is the correct one).
Yes, use arctan.

3. Aug 24, 2011

### Staff: Mentor

Since the vectors aren't in the same direction, you can't simply add their magnitudes.
This is fine.
Yes. Depending on the mode your calculator is in, you'll get an answer in degrees or radians. To answer the question of the problem, you will probably need to say something like "10 degrees north of west" or "at a heading of 280 degrees." These are just examples, though.

4. Aug 24, 2011

### dGasim

I have gotten the first part of the question right. But when it comes to second one. I did arctan(23/3) which gave me 82.6*. But I am not sure of the direction in this case because the question wants the input as "direction N _____ *W"

btw. * = degrees in this case.

5. Aug 24, 2011

### tiny-tim

Hi Gasim!

(have a degree: ° )
the number you have to fill in is the number of degrees from North to the direction …

the direction is that number of degrees West of North

6. Aug 24, 2011

### dGasim

Thanks a lot!! Got every question right because of you guys!! :)