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he66666
 5 years ago
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
 5 years ago
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?

This Question is Closed

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So we denote force that small exert as x

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0that mean larger boat exerts 2x maganitude of force

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Do you have a picture or diagram?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1you can add your vectors to get the direction of motion..right?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1as 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
 5 years ago
Best ResponseYou've already chosen the best response.0I 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
 5 years ago
Best ResponseYou've already chosen the best response.1vectors can move around the graph; they arent anchored to one spot

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1vectors are simply direction and magnitude with no regard to initial position....

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1we add vectors by stacking them head to tail and drawing a new vector from the start to the end...

he66666
 5 years ago
Best ResponseYou've already chosen the best response.0yes, but if it's two tugs towing a ship, shouldn't the diagram be a triangle with the two tensions?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1it 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
 5 years ago
Best ResponseYou've already chosen the best response.0oh I understand now. So after I draw the parallelogram, what do I do?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1well, that gives you an idea of whats going on; the real eat is in deciphering the angles for the information they can give...

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1one vector is twice the other, so we can use 1 and 2 as magnitudes....length of the vectors right?

he66666
 5 years ago
Best ResponseYou've already chosen the best response.0so the length of the vectors represent tension?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1the length represent force, whatever you wanna call it :)

he66666
 5 years ago
Best ResponseYou've already chosen the best response.0oh ok. sorry for asking so many questions, I'm not good at vectors :/

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1lets start getting some sin and cos number to define these vector better....

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1vector small = <cos15,sin15> vector large = <2cos20, 2sin20> you see why?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1vs=<.9659, .2588> vl = <1.8794, .6840> now we add them like we did in the picture but this time its simply the numbers

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1.9659, .2588 1.8794, .6840  <2.8453, .4252> is the direction and length of our new vector

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1we take the inverse tangent of these number to find the angle created....and hopefully its right :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.18.499 = 8.499 we good with it? do you see what i did ?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1<x,y> is what our new vector lloks like. y/x = tan(angle) tan^1(y/x) = angle

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1if theres another way to get to that, fine; but thats how id do it cause it works lol

he66666
 5 years ago
Best ResponseYou've already chosen the best response.0Oh, I see. I get it now! thanks a bunch :D
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