A man wishes to cross a river in a boat. If he crosses the river in minimum time, he takes 10 minutes with a drift of 120m. If he crosses the river taking shortest route, he takes 12.5 minutes, find the velocity of the boat with respect to water.
A
20m/min
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B
12m/min
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C
10m/min
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D
8m/min
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Solution
The correct option is A20m/min Let L be the width of the river u be the speed of river and v be the speed of man w.r.t water.
For shortest time path, t=10=Lv...(i)
For shortest distance path,
t=12.5=L√v2−u2=Lv√1−u2/v2...(ii)
Give Drift =120m in 12min. So, river velocity u=12012=10m/min
Dividing (i) by (ii), 1012.5=Lv×v√1−u2/v2L ⇒45=√1−122v2 ⇒1625=1−122v2 ⇒122v2=1−1625=925 ⇒12v=35 ⇒v=12×53=20m/min