Babynini
  • Babynini
Vectors.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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Babynini
  • Babynini
1 Attachment
Babynini
  • Babynini
@iambatman :)
Babynini
  • Babynini
ganeshie it's kind of the same thing we just did except for without angles given.

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More answers

ganeshie8
  • ganeshie8
draw both the velocity vectors break them into component form and simply add them up
Babynini
  • Babynini
|dw:1433310949412:dw|
Babynini
  • Babynini
wait, I forgot the component form.
ganeshie8
  • ganeshie8
|dw:1433311043791:dw|
Babynini
  • Babynini
so 19
ganeshie8
  • ganeshie8
Nope, you need to add the respective components
ganeshie8
  • ganeshie8
x components : -5+0 = -5 y components : 0+24 = 24 so the resultant velocity vector with reference to water is -5i+24j
Babynini
  • Babynini
haha right. sorry. So now how do we change that to decimal numbers? (note how the first question wants to be answered)
ganeshie8
  • ganeshie8
simply take magnitude of the resultant velocity vector for speed
ganeshie8
  • ganeshie8
speed = \(\|-5i+24j\|=\sqrt{(-5)^2+24^2}=?\)
Babynini
  • Babynini
\[\sqrt{601}\] =24.52
ganeshie8
  • ganeshie8
looks good
Babynini
  • Babynini
fabulous. part next? :)
ganeshie8
  • ganeshie8
work the angle for any vector \(xi+yj\) the angle with the positive x axis is given by \(\tan^{-1}(y/x)\)
Babynini
  • Babynini
so since the five is negative..do i carry the negative with it?
Babynini
  • Babynini
78.23
ganeshie8
  • ganeshie8
try 11.77 for angle
Babynini
  • Babynini
yeah that worked :P
Babynini
  • Babynini
how did you get there?
ganeshie8
  • ganeshie8
you got angle = \(-78.23\) right, it is negative
ganeshie8
  • ganeshie8
in which quadrant does the angle \(-78.23\) lies in ?
Babynini
  • Babynini
4
ganeshie8
  • ganeshie8
yes, but the resultant vector lies in 2nd quadrant : |dw:1433312298520:dw|
ganeshie8
  • ganeshie8
so you need to add 180 to the angle given by your calculator : \[-78.23+180=?\]
Babynini
  • Babynini
101.77
ganeshie8
  • ganeshie8
Yes thats the angle from positive x axis : |dw:1433312428785:dw|
ganeshie8
  • ganeshie8
but the question is asking for the angle from N : |dw:1433312468055:dw|
Babynini
  • Babynini
oh oh i see.
Babynini
  • Babynini
so that - 90 which comes out to 11.77
ganeshie8
  • ganeshie8
thats it! with \(\tan^{-1}\) function you always need to check if 180 degrees needs to be added based on the quadrant of the actual point
Babynini
  • Babynini
so if it's negative then always yes add 180 yeah? :P
ganeshie8
  • ganeshie8
not quite
ganeshie8
  • ganeshie8
tell me this in which quadrant does the point (-1, 1) lie in ?
Babynini
  • Babynini
2
ganeshie8
  • ganeshie8
so would you trust me if i say the angle is -45 with positive x axis ?
ganeshie8
  • ganeshie8
try working the angles using arctan(y/x) formula for below points : (1, 1) (-1, 1) (1, -1) (-1, -1)
Babynini
  • Babynini
45 -45 -45 45
ganeshie8
  • ganeshie8
do they make sense ?
ganeshie8
  • ganeshie8
look at the last point and last angle : (-1, -1) 45 how can a point in III rd quadrant make an angle 45 ?
Babynini
  • Babynini
yeah.
Babynini
  • Babynini
these are good questions to think about :o
ganeshie8
  • ganeshie8
it doesn't make sense, so you need to add 180 to 45 : 45+180 = 225 so the angle made by vector (-1, -1) is 225 and not 45 ok
ganeshie8
  • ganeshie8
\(\tan^{-1}(y/x)\) formula gives you correct angle when the point is in I or IV quadrants
Babynini
  • Babynini
for III and II add 180?
ganeshie8
  • ganeshie8
When th point lies in II or III quadrants, you need to add 180 degrees to the answer given by your calculator
ganeshie8
  • ganeshie8
In our case, the point (-5, 25) is in II quadrant so we added 180 degrees to the answer given by calculator
ganeshie8
  • ganeshie8
this is one of the things that trips all students when they begin to learn inverse trig functions
Babynini
  • Babynini
yeah man, i'm kind of trippin now haha but I think I get it.
ganeshie8
  • ganeshie8
watch this video if u have time https://www.khanacademy.org/math/trigonometry/unit-circle-trig-func/inverse_trig_functions/v/inverse-trig-functions-arctan
ganeshie8
  • ganeshie8
not now, when ever you have time and feel like... it explains arctan function very nicely
Babynini
  • Babynini
Thanks :)

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