Question

Suppose you walk 15 m in a direction exactly 25° south of west then you walk 22.5 m in a direction exactly 45° west of north.
What is the angle of the compass direction of a line connecting your starting point to your final position measured South of West in degrees?
Repeat part (a) by finding your distance from the starting point in m, but reverse the order of the two legs of the walk. That is, you first walk leg B, which is 22.5 m in a direction exactly 45° west of north, and then leg A, which is 15 in a direction exactly 25° south of west.
What is the angle of the compass direction o

Answer 1

*What is the angle of the compass direction of a line connecting your starting point to your final position measured South of West in degrees?

Answer 2

I keep getting an angle of either 342 degrees or 162 degrees, one of which is east of south and the other is west of north...
@LastDayWork

Answer 3

OOH, I know what I screwed up on.
Ok
@jhc2014 are you familiar with vectors/ vector components?

Answer 4

Write the two steps as vectors (in polar form).

Answer 5

not to familiar and not sure what polar form is

Answer 6

how would you get the angle of the compass from that? what formula would you have to use

Answer 7

ok, you'll have to break the vectors into their x and y components

Answer 8

that be 22.5cos(45)+15cos(25) for x right and 22.5sin(45)+15sin(25) for y right ?

Answer 9

you're VERY close

Answer 10

ok, first, for the x-axis, if you're right of the y-axis, then your numbers are positive, if you're on the left, the numbers are negative

second, the angles 25 and 45 that you're given are relative. you have to start from the horizontal for your angles. so for example, the first vector that is "25". That starts from the negative x-axis. You need to add 180 so that you start from the positive x-axis.

So the two questions you need to ask are:
Is the vector component positive or negative?
How do I modify the angles so that they include the FULL angle?

Answer 11

In my explanation, I didn't include the y-component. I want to see if you can figure that out.

Answer 12

y component=22.5sin(45)+15sin(205)?

Answer 13

-15 sin(205) +22.5 sin (90 + 45)

Answer 14

good attempt though.
Does that make sense?

Answer 15

yes the angle is the vector itself right

Answer 16

ok so now you have your x and y
to get your new angle
tan^-1 (y/x)

Answer 17

41.7 degrees

Answer 18

never mind i made a calculation error -84.1 degrees?

Answer 19

x-component: 29.505
y=component 22.249

Answer 20

Your components are off

Answer 21

37.01905419 my x component was wrong

Answer 22

having the angle how would you find the distance from the starting point in meters but reverse the order of the two legs of the walk. That is, you first walk leg B, which is 22.5 m in a direction exactly 45° west of north, and then leg A, which is 15 in a direction exactly 25° south of west.?

Answer 23

use the pythagorean theorem

Answer 24

you should get 36.95 right

Answer 25

yes

Answer 26

when i went to put it in it said it was wrong

Answer 27

in what?

Answer 28

my online homework site

Answer 29

were ALL the answers wrong?

Answer 30

no the other ones were right

Answer 31

so just the length of the reverse?

Answer 32

yes

Answer 33

is this due immediately? I'm trying to figure out what we did wrong...

Answer 34

no not immediately

Answer 35

to be honest i have no idea why the Pythagorean therom didnt work

Answer 36

maybe sig figs?

Answer 37

i tried sigfigs but used my last attempt and the right answer was 31.02 so we were really close but i appreciate all the help youve given me wouldnt have been able to get it done without you thank you

Answer 38

oh, you only had a fixed number of tries??
I'm sorry

Answer 39

its not problem still got the others right no problem at all thanks again