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).
.

Answer

250

Explanation

As we know that light travels in path such as to reach from one point to another in shortes 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^(@)`
`therefore AQ=10 Km.`
For `P` to `A` :
`t_(1)=(5)/(3)`
From `A` to `Q`: `t_(2)=(10)/(4)=(5)/(2)`
`T=t_(1)+t_(2)=(5)/(2)=(25)/(6)hr.=250 minutes`