Question

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?

Answer 1

So we denote force that small exert as x

Answer 2

that mean larger boat exerts 2x maganitude of force

Answer 3

Do you have a picture or diagram?

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

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

Answer 14

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

Answer 15

so the length of the vectors represent tension?

Answer 16

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

Answer 17

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

Answer 18

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

Answer 19

vector small = <cos15,sin15>

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

Answer 20

vs=<.9659, .2588>

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

Answer 21

Yes, i'm following

Answer 22

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

Answer 23

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

Answer 24

|-8.499| = 8.499 we good with it?

do you see what i did ?

Answer 25

yup :)

Answer 26

<x,y> is what our new vector lloks like.

y/x = tan(angle)

tan^-1(y/x) = angle

Answer 27

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

Answer 28

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

Answer 29

yw :)