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A man crosses a river in a boat. If he c...

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

Text Solution

Verified by Experts

The correct Answer is:
`200m, 20m//min, 12m//min`
For minimum time
`t = (d)/(v_(B)) rArr 10 = (d)/(v_(B)) …(1)`
driff `120 = v_(w) xx 10 rArr v_(w) = 12m//min`
For shortest path
`sqrt(v_(B)^(2)-v_(A)^(2)) = (d)/(12.5) rArr sqrt(v_(B)^(2)-12^(2)) = (2d)/(25) …(2)`
from (1) & (2)
`sqrt(v_(B)^(2)-144) = (2xx10V_(B))/(25) rArr v_(B)^(2-) 144 = (16V_(B)^(2))/(25)`
`(3)/(5) v_(B) = 12 rArr v_(B) = 20m//s rArr d = 10v_(B) = 200m`
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