WEBVTT
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This is Giancoli Answers
with Mr. Dychko.
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We want to know the velocity of
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Huck Finn with respect to the river bank
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so we need to add the velocity of Huck Finn
with respect to the river
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plus the velocity of the river
with respect to the bank
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and the inner subscript's are the same here,
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they are both *R*—river—and so
they disappear
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and we are left with *H* and *B*
in our answer;
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Huck Finn with respect to the bank
which is what we want.
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And so we have the two vectors here
that we know;
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one is Huck Finn with respect to the raft—
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0.7 meters per second straight
across the river—
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and then we know the velocity of the river
with respect to the bank
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which is 1.5 meters per second
downstream
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and this red vector is the resultant;
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this is the velocity of Huck Finn
with respect to the river bank.
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So the speed or the magnitude
of the velocity
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is the square root of the sum of
the squares of these two
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velocities here
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so that's the square root of 0.7
meters per second squared
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plus 1.5 meters per second squared
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that gives 1.6553 meters per second
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so that's the magnitude of the velocity.
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And then the direction
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let's say we have *Θ* in here
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between the resultant and straight across
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that would make *tan*
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that angle would be the opposite
over the adjacent
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and then the angle then is
the inverse tangent
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of that opposite 1.5 meters per second
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divided by the adjacent which is
0.7 meters per second
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which is about 65 degrees
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and you have to specify
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what you are measuring your angle
with respect to
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because it's equally valid
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I mean it's always valid to measure your
angle with respect to whatever you like
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but I could imagine somebody could also
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put an angle here with respect
to the river bank
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and that would be the complement
of this angle 25 degrees
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but what we have chosen to do here is
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65 degrees with respect to straight across.
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So our answer is velocity of Huck Finn
with respect to the bank
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is 1.66 meters per second,
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65 degrees downstream from
straight across.
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And I have to say downstream because
well, if I just say 65 degrees,
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this would also be 65 degrees here
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and so I have to say downstream whereas
this would be 65 degrees upstream.