River stream velocity grows in proportion to the distance from the bank and reaches its maximum velocity 2 m/s in the middle. Near the bank, the velocity is zero. The speed of swimmer in still water is 5 m/s and directed perpendicular to the river stream. The width of the river is 100 m the drifting in swimmer is 5n metre. Find the value of n.

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answer is 4.

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Detailed Solution

Time taken to reach the middle of the river form the river bank, $t= \frac{50}{5} 10 sec$
Now, $V_{x} = (\frac{2}{10}) t$
$\int_{0}^{x} dx= \frac{1}{5} \int_{0}^{10} tdt$
$x = 10 m$
Hence total difference $=10×2=20 m$ .

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