A man crosses a river in a boat. If he cross the river in minimum time he takes `10 min` with a drift `120 m.` If he crosses the river taking shortest path, he takes `12.5 min,` find
(a) width of the river
(b) velocity of the boat with respect to water
(c) speed of the current

Options

A. `20m//mi n`
B. `212m//mi n`
C. `10m//mi n`
D. `8m//mi n`

Answer

a

Explanation

`10=L/v.......(i)`
`12.5=L/(sqrt(v^(2)-u^(2)))=L/(vsqrt(1-u^(2)//v^(2)))......(ii)`
From (i) and (ii) `1/12.5=L/vxx(vsqrt(1-u^(2)//v^(2)))/L`
`4/5=sqrt(1-(12^(2))/(v^(2)))`
`16/25=1-(12^(2))/(v^(2))=1-16/25=9/25`
`12/v=3/5 implies v=(12xx5)/3=20m//s`