A man crosses the river in a boat .if he cross the river in minimum time he takes 10 min with a drift 120m .if he crosses the river taking shortest path,he takes 12.5min,find width of the river,velocity of the boat with respect to water,speed of the current
Final Answer : (a) 200 m
(b) 1/3 m/s
(c) 0.2 m/s
Steps:
1) We are assuming respective velocities are same in both cases and u > v. (see below)
Case 1 : (Crossing in Minimum Time)
=> When man wants to cross the river in minimum time, then he must swim perpendicular to flow of river.
Let the relative velocity of man wrt river be 'v' &
Velocity of river /Speed of current be 'u'.
d - Width of River
2) Time taken to cross the river in minimum time :
Drift = u * t
=> 120 m = u * 600
=> u = 0.2m/s
Therefore,
(c) Speed of current = 0.2m/s
(3) We can also, say :
4) Case - 2 (Crossing with shortest Path) :
Let the relative velocity 'v' make an angle with vertical in this case .
For Drift to be minimum, (as v < u)
Horizontal component of 'v' must equal to speed of river.
That is,
.
5) Now,
We can say,
6) Now,
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