Grade 12 math: vectors as forces?
Two tugs are towing a ship. The smaller tug is 15 degrees off the port bow, and the larger tug is 20 degrees off the starboard bow. The larger tug pulls twice as hard as the smaller tug. In what direction will the ship move?
answer: 8.5 degrees to the starboard side
I really don't get how you solve this question. Can someone please explain the solution?

- he66666

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- anonymous

So we denote force that small exert as x

- anonymous

that mean larger boat exerts 2x maganitude of force

- anonymous

Do you have a picture or diagram?

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## More answers

- amistre64

you can add your vectors to get the direction of motion..right?

- amistre64

##### 1 Attachment

- amistre64

as you can see, i added one vector to the end of the other, and where it ends up pointing is our new direction of travel

- he66666

I stil don't understand.. how did it turn into a parallelogram? our teacher told us to use the position diagram and the vector diagram.. :S

- amistre64

vectors can move around the graph; they arent anchored to one spot

- amistre64

vectors are simply direction and magnitude with no regard to initial position....

- amistre64

we add vectors by stacking them head to tail and drawing a new vector from the start to the end...

- he66666

yes, but if it's two tugs towing a ship, shouldn't the diagram be a triangle with the two tensions?

##### 1 Attachment

- amistre64

it is, the initial positions are to the left and right of the ship; then i took one vetor and added it to the other to determine the direction of travel when both forces are applied

- he66666

oh I understand now. So after I draw the parallelogram, what do I do?

- amistre64

well, that gives you an idea of whats going on; the real eat is in deciphering the angles for the information they can give...

- amistre64

one vector is twice the other, so we can use 1 and 2 as magnitudes....length of the vectors right?

- he66666

so the length of the vectors represent tension?

- amistre64

the length represent force, whatever you wanna call it :)

- he66666

oh ok. sorry for asking so many questions, I'm not good at vectors :/

- amistre64

##### 1 Attachment

- amistre64

lets start getting some sin and cos number to define these vector better....

- amistre64

vector small =
vector large = <2cos20, 2sin20> you see why?

- amistre64

vs=<.9659, .2588>
vl = <1.8794, -.6840> now we add them like we did in the picture but this time its simply the numbers

- he66666

Yes, i'm following

- amistre64

.9659, .2588
1.8794, -.6840
-------------
<2.8453, -.4252> is the direction and length of our new vector

- amistre64

we take the inverse tangent of these number to find the angle created....and hopefully its right :)

- amistre64

|-8.499| = 8.499 we good with it?
do you see what i did ?

- he66666

yup :)

- amistre64

- amistre64

if theres another way to get to that, fine; but thats how id do it cause it works lol

- he66666

Oh, I see. I get it now! thanks a bunch :D

- amistre64

yw :)

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