What should be the minimum velocity of boat with respect to the river so that starting from point A the boat reaches point C on the opposite bank. Velocity of river flow is V r .
Text Solution
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Method 1 :
= 
= 
+ 
(V net ) x = V r – V br sin θ
(V net ) y = V br cos θ
Time taken to cross the river
T = 
= 
Drift BC = (V net ) x t
a = BC = (V r – V br sin θ ) 
V br = 
………..(i)
For V br to minimum
= 0
i.e., 
= 0
tan θ = tan θ 0 = 
…………..(ii)
Putting (ii) in (i)
(V br ) min = 
(V br ) min = 
Method 2 :
From 
= 
+ 
Draw a vector triangle. Draw a perpendicular from tip of V r on line of V net . That will give minimum V br , because minimum distance is perpendicular distance.
From Vector triangle
(V br ) min = V r sin θ 0
(V br ) min = V r 
Since from figure tan θ 0 = 
.
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