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A man starting from point P cross a 4km ...

A man starting from point `P` cross a 4km wide lagoon and reaches point `Q` in the shortest possible time by the path shown in the figure. If the person swims at a speed of 3km//hr and walks at a speed of 4km//hr, then find his time fo journey (in minutes).
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Text Solution

Verified by Experts

The correct Answer is:
B

As we know that light travels in a path such as to reach from one point to another in shortest possible time.
Therefore, the man must travel along that path on which light would have travelled in moving from `P` to `Q`
By Snell's law
`(sin i)/(sin r)=(mu_(2))/(mu_(1)) rArr sin r=(mu_(1))/(mu_(2)),sin i`
`sin r=(3)/(5),"(4)/(3)=(4)/(5)`
`rArr r = 53^(@)`
`AQ = 10 km`
From `P` to `A` :
`t_(1) = (5)/(3)`
From `A` to `Q : t_(2) = (10)/(4) =(5)/(2)`
`T=t_(1)+t_(2)=(5)/(3)+(5)/(2)=(25)/(6)hr.=250` minutes.
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