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# Not doing too well at this one :/

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Hello.

I've been working at a 2D kinematics problem for a couple of days now, trying to work out how to do it:

you can view it here:

http://physics.stackexchange.com/questions/101508/finding-an-equation-to-solve-for-the-velocity-of-a-swimmer-crossing-a-river

I've worked out the idea of how to get the answer, however I just can't seem to get there.

I was hoping someone could explain how they went from step 1 to step 2. I can see some factoring going on but just can't quite work it out.

vest4R  Mar 23, 2017
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Step 1: $$d_2\cdot v_s\cdot\cos 45^{\circ}=d_1\cdot(v_r-v_s\sin45^{\circ})$$

They multiplied out the bracket on the right hand side:

$$d_2\cdot v_s\cdot\cos 45^{\circ}=d_1\cdot v_r-d_1 \cdot v_s\sin45^{\circ}$$

and then they add d1 . vs sin45 each side:

$$d_2\cdot v_s\cdot\cos 45^{\circ}+d_1 \cdot v_s\sin45^{\circ}=d_1\cdot v_r$$

Factor out the common factor(vs):

$$v_s\cdot(d_2\cdot\cos 45^{\circ}+d_1\sin 45^{\circ})=d_1\cdot v_r$$ <-- Step 2!!

MaxWong  Mar 23, 2017

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