12. A boat can go across a lake and...
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12. A boat can go across a lake and return in time T at a speed V. On a rough day there is uniform cum at speed u to help the onward journey and impede the return journey. If the time taken to go across and return on the rough day be T, then T/T= (0) 1 - 3 (B) - (C)1 + 2 (D)_1_ 1 - 1

JEE/Engineering Exams
Physics
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Let the distance of the trip (go across and return) is ( D ), then the travel time in calm day is: ( T_{0}=frac{D}{V}+frac{D}{V}=frac{2 D}{V} ) the travel time in rough day is: ( T=frac{D}{V+v}+frac{D}{V-v}=frac{D(V-v+V+v)}{(V+v)(V-v)}=frac{2 D V}{(V+v)(V-v)} ) ( (2) div(1): ) ( frac{T}{T_{0}}=frac{2 D V}{(V+v)(V-v)} cdot frac{V}{2 D}=frac{V^{2}}{V^{2}-v^{2}}=1-frac{V^{2}}{v^{2}} ) Answer: ( frac{T}{T_{0}}=1-frac{V^{2}}{v^{2}} )
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