+251 
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.
Thank you for your help.
+9673 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!!
