Question:
Velocity of a man in still water is v and the velocity of the stream is w. he reaches the opposite bank in the time T1. To swim same distance along the river he takes time T2. show that T1/T2=root over(v+u/v-u)
Answer:
Let the velocity of man be v and velocity of stream be u; Relative velocity downstream = u+v ; Relative velocity upstream = v-u
Let the distance covered be x in a time T1 downstream at a velocity v+u
In the upstream with relative velocity u-v, let the time taken to cover the same distance covered x be T2
Time = Distance / Speed
Hence, T1 = x / u+v and , T2 = x / v-u
Dividing T1 and T2 we get , T1 / T2 = x / v+u divided by x / v-u = v+u / v-u
NOTE: The answer is not root over (v+u / v-u) but (v+u / v-u)
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