River stream velocity grows in proportion to the distance from the bank and reaches its maximum velocity 2 ms-1 in the middle. Near the bank velocity is zero. The velocity of a swimmer in still water is 5 ms-1 and is directed perpendicular to river stream. The width of river is 100 m. The drifting in swimmer is 5n meter. The value of n is ______.
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answer is 4.
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Detailed Solution
vx=ky and vy=5∴ y=5t, At middle point, 50=5t∴ t =10s∵ vx=ky At middle, vx=2∴k=250∴ vx=250y=y25=5t25=t5⇒ dxdt=t5⇒ ∫0x0 dx=∫010 t5dt∴ x0=10m up to middle ∴ Total drifting =2×10=20m∴ 5n=20,n=4