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Mathematics 49 Online
OpenStudy (anonymous):

Rita can swim 3m/s in still water. The current of a river is 1 m/s. If Rita wishes to swim across the river and land at a point directly opposite her starting position, in what direction should she head? How long would it take her to swim across the river if the river is 100 m wide?

OpenStudy (anonymous):

|dw:1363469478642:dw|

OpenStudy (anonymous):

how do I calculate this? and where is the river?

OpenStudy (anonymous):

assume current is along +ve X-axis and resultant motion to swim along +ve Y-axis \[v_w=1\hat{i}\\ v_s=3(-cos\theta\hat{i}+sin\theta\hat{j})\\ v_r=v\hat{j} \] by vector addition, \[v_r=v_s+v_w\] solve x and y components

OpenStudy (anonymous):

oh so you're using the unit vectors! which angle do I use to sub in for theta?

OpenStudy (anonymous):

you find the angle by equating the x-components

OpenStudy (anonymous):

um how do I do that? :$ sorry vectors are really confusing to me :(

OpenStudy (anonymous):

subtitute in my 4th eq. the vectors from above 3

OpenStudy (anonymous):

\[v\hat{j}=-3\cos\theta\hat{i}+3\sin\theta\hat{j}+\hat{i} \]

OpenStudy (anonymous):

now, on the right hand part, put the i-hat terms together and j-hat terms together.

OpenStudy (anonymous):

Oh ok I got that so what do I do after? :O

OpenStudy (anonymous):

write it here so i can guide ya

OpenStudy (anonymous):

alright so it would be -3costheta i-hat ^2 + 3sintheta j-hat ?

OpenStudy (anonymous):

no multiplications... \[ 0\hat{i}+v\hat{j}=(1-3\cos\theta)\hat{i}+3\sin\theta\hat{j}\\ \therefore 0=1-3\cos\theta\qquad v=3\sin\theta \] use the first to get θ and use it in second to get your v tada

OpenStudy (anonymous):

θ is the direction Rita should swim in. and for the second, you have distance and speed (v), find time

OpenStudy (anonymous):

which one is distance? and thank you so much for helping me! :) I got the first half but I'm unsure as to what distance is :(

OpenStudy (anonymous):

given in the problem.. 100m wide river

OpenStudy (anonymous):

OOOOOHHHH! LOL thanks :P I can be so dumb at times :/

OpenStudy (anonymous):

I know that state

OpenStudy (anonymous):

Hehehe it's what happens when I procrastinate during the march break :$ you're awesome :D

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