Babynini
  • Babynini
A river is flowing due east at 8 mi/hr. A man heads his motorboat in the direction N30E in the river. the speed of the motorboat relative to the water is 12mi/hr a)express the true velocity of the motorboat as a vector b) find the true speed and direction of the motor boat.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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Babynini
  • Babynini
@zepdrix free? (:
Babynini
  • Babynini
@jim_thompson5910 whenever you're free, please! :)
jim_thompson5910
  • jim_thompson5910
|dw:1434672450418:dw|

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jim_thompson5910
  • jim_thompson5910
Draw in a parallelogram |dw:1434672391987:dw|
jim_thompson5910
  • jim_thompson5910
this vector, ie the resultant vector, is the boat's true path |dw:1434672449672:dw|
Babynini
  • Babynini
oo ok
Babynini
  • Babynini
Following so far
Babynini
  • Babynini
and the resultant is w = u + v right?
jim_thompson5910
  • jim_thompson5910
what is the vector component form for the vector pointing directly east (the river current)?
Babynini
  • Babynini
emm v = 0i + 8j ?
jim_thompson5910
  • jim_thompson5910
close
jim_thompson5910
  • jim_thompson5910
that's pointing north though
Babynini
  • Babynini
oops sorry v= 8i + 0j
jim_thompson5910
  • jim_thompson5910
correct
jim_thompson5910
  • jim_thompson5910
what is the boat's vector (ignore the current) ?
jim_thompson5910
  • jim_thompson5910
hint: |dw:1434672891389:dw|
Babynini
  • Babynini
Um..not sure
jim_thompson5910
  • jim_thompson5910
z = x*i + y*j x = r*cos(theta) y = r*sin(theta) theta = 60 degrees r = 12
Babynini
  • Babynini
x = 6 y = (12 sq3)/2
jim_thompson5910
  • jim_thompson5910
or y = 6*sqrt(3)
Babynini
  • Babynini
or y = 6 sq3
jim_thompson5910
  • jim_thompson5910
yep
Babynini
  • Babynini
haha yes
jim_thompson5910
  • jim_thompson5910
so that's the boat's vector <6, 6*sqrt(3)>
jim_thompson5910
  • jim_thompson5910
|dw:1434673336710:dw|
jim_thompson5910
  • jim_thompson5910
|dw:1434673363432:dw|
Babynini
  • Babynini
so is it = <14, 6 sq3>
jim_thompson5910
  • jim_thompson5910
yes, that's u+v
jim_thompson5910
  • jim_thompson5910
which is also the true velocity vector of the boat
Babynini
  • Babynini
yaaay! Now part b :)
jim_thompson5910
  • jim_thompson5910
true speed = |u+v| true direction = direction of vector u+v
Babynini
  • Babynini
Direction = 2 sq76 ?
Babynini
  • Babynini
or 4 sq19
jim_thompson5910
  • jim_thompson5910
4*sqrt(19) is the magnitude of u+v so it is the true speed
Babynini
  • Babynini
o right. Direction: (theta) = arctan( (6sq3)/14)
Babynini
  • Babynini
so.. 36.58?
Babynini
  • Babynini
but if we want to find it from x it would be that subtracted from 180 correct?
Babynini
  • Babynini
sorry, I meant 90
Babynini
  • Babynini
Which would be 53.41
Babynini
  • Babynini
N53E
jim_thompson5910
  • jim_thompson5910
yeah I'm getting theta = 36.58677555 so 90 - theta = 90 - 36.58677555 = 53.41322445
Babynini
  • Babynini
Yay, it matches :)
Babynini
  • Babynini
a) velocity of motorboat: <14, 6*sq3> b) Speed: 17.44 Direction: N53.4E
jim_thompson5910
  • jim_thompson5910
everything looks good
Babynini
  • Babynini
thank you
jim_thompson5910
  • jim_thompson5910
yw

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