A) \[(2-\sqrt{3})\,V\]
B) \[2(2-\sqrt{3})\,V\]
C) \[4\,(2-\sqrt{3})\,V\]
D) \[(2+\sqrt{3})\,V\]
Correct Answer: C
Solution :
Drift = d/2 \[\frac{d}{2}=({{V}_{r}}-{{V}_{s}}\,\sin \,{{30}^{o}})\,d/Vs\,\cos \,{{30}^{o}}\] \[\frac{d}{2}=\left( V-\frac{{{V}_{s}}}{2} \right)\frac{d}{{{V}_{s}}\sqrt{3/2}}\] \[\frac{d}{2}=\left[ \frac{2V-{{V}_{s}}}{2}\,\frac{2d}{\sqrt{3}{{V}_{s}}} \right]\] \[\sqrt{3}{{V}_{s}}=9V-2{{V}_{s}}\] \[\left( \sqrt{3}+2 \right){{V}_{s}}=4V\] \[{{V}_{s}}=\frac{4}{\sqrt{3}+2}V=\frac{4(2-\sqrt{3})}{\left( \sqrt{3}+2 \right)\,\left( 2-\sqrt{3} \right)}V\]\[\Rightarrow \] \[{{V}_{S}}=4\,(2-\sqrt{3})V\] Here =VmG = Velocity of swimmer respect to ground VrG = velocity of river with respect to ground and Vmr= velocity of swimmer with respect to river.2You need to login to perform this action.
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