A man in a boat crosses a river from point A. If he rows perpendicular to the banks then, 10 minutes after he starts, he will reach point C lying at a distance S = 120 m downstream from point B. If the man heads at a certain angle α to the straight line AB (AB is perpendicular to the banks) against the current he will reach point B after 12.5 minutes. Assume the speed of the boat relative to the water to be constant and of the same magnitude in both cases.
(i) Width of the river λ is–
Text Solution
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Ans.
(i)
Sol. 200 m
(ii)
Sol. 20 m/min
(iii)
Sol.
Speed of current = 
= 
= 12 m/min
When boat moves along AB
t = 
(v = velocity of boat with respect to river)
10 min = 
….(1)
In second case
t AB = 
= 12.5 min
cos α = 
= 
α = 37º
v sin α – u = 0
v = 
= 
= 20 m/min
AB = v × 10 min = 20 m/min × 10 m
AB = 200 m
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