anonymous
  • anonymous
How do I solve these types of problems? 'A ferry heads west across a river. It travels 20 miles per hour in still water. The river flows south at 15 miles per hour. In which direction will the ferry actually travel. How fast will it travel?' I need someone to explain this, so that I can do the other problems like it.
Mathematics
katieb
  • katieb
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amistre64
  • amistre64
its a vector related problem
amistre64
  • amistre64
1 Attachment
amistre64
  • amistre64
add the vector to get the red travel distance vector

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amistre64
  • amistre64
<20,0> is the westward vector ; and <0,-15> is the southward vector
amistre64
  • amistre64
the new vector is simply: <20,0> <0,-15> -------- <20,-15>
amistre64
  • amistre64
the direction traveled is the tan^-1 (y/x) + pi
amistre64
  • amistre64
-15/20 = -3/4 tan^-1(-3/4) =abt 233.13 degrees if i did it right
amistre64
  • amistre64
had to add 270 to it to get itin the proper qudrant
amistre64
  • amistre64
and the distance traveled is just the pythag of the y and x components
amistre64
  • amistre64
any of this make sense?
anonymous
  • anonymous
No...I wish though.
amistre64
  • amistre64
hmm.... a vector is just an arrow that points in any direction and indicates the distance traveled; they can be called directed line segments
amistre64
  • amistre64
when we add them, they form a new arrow that measures a new direction and length
amistre64
  • amistre64
you essentially have the ferry being thrown off course by the river; by 15 meters every sec right?
amistre64
  • amistre64
well; 15 miles for every hour travled
amistre64
  • amistre64
if we pythag the new direction; we get 20 west; and 15 south; those are the legs of a triangle and the distance actually covered in one hour is the hypotenuse of that triangle
amistre64
  • amistre64
sqrt(20^2 + 15^2) = distance traveled in one hour
amistre64
  • amistre64
in this case; its moved 25 miles in one hour...... or 25 mph
amistre64
  • amistre64
the direction it moved is to the south and west...measured from some starting point; usually idicated as due est
amistre64
  • amistre64
due east is the inital starting point of angle measures...
amistre64
  • amistre64
any of this ringing bells yet :)
anonymous
  • anonymous
I understand better now, thank you for helping me so much :)

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