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?

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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?

Mathematics
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So we denote force that small exert as x
that mean larger boat exerts 2x maganitude of force
Do you have a picture or diagram?

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you can add your vectors to get the direction of motion..right?
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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
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
vectors can move around the graph; they arent anchored to one spot
vectors are simply direction and magnitude with no regard to initial position....
we add vectors by stacking them head to tail and drawing a new vector from the start to the end...
yes, but if it's two tugs towing a ship, shouldn't the diagram be a triangle with the two tensions?
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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
oh I understand now. So after I draw the parallelogram, what do I do?
well, that gives you an idea of whats going on; the real eat is in deciphering the angles for the information they can give...
one vector is twice the other, so we can use 1 and 2 as magnitudes....length of the vectors right?
so the length of the vectors represent tension?
the length represent force, whatever you wanna call it :)
oh ok. sorry for asking so many questions, I'm not good at vectors :/
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lets start getting some sin and cos number to define these vector better....
vector small = vector large = <2cos20, 2sin20> you see why?
vs=<.9659, .2588> vl = <1.8794, -.6840> now we add them like we did in the picture but this time its simply the numbers
Yes, i'm following
.9659, .2588 1.8794, -.6840 ------------- <2.8453, -.4252> is the direction and length of our new vector
we take the inverse tangent of these number to find the angle created....and hopefully its right :)
|-8.499| = 8.499 we good with it? do you see what i did ?
yup :)
is what our new vector lloks like. y/x = tan(angle) tan^-1(y/x) = angle
if theres another way to get to that, fine; but thats how id do it cause it works lol
Oh, I see. I get it now! thanks a bunch :D
yw :)

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