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A man wishes to swim across a river 600m wide .If he can swim at the rate of 4km/hr in still water and the river flows at 2km/hr .Then in what direction must he swim to reach a point exactly opposite to the starting point and when will he reach it?

A man wishes to swim across a river 600m wide .If he can swim at the rate of 4km/hr in still water and the river flows at 2km/hr .Then in what direction must he swim to reach a point exactly opposite to the starting point and when will he reach it?

Grade:11

1 Answers

Piyush Kumar Behera
417 Points
7 years ago
First of all,
4kph = (4/3.6) = 1.1m/sec. 
2kph = (2/3.6) = 0.55m/sec. 
To cross directly across the river, he must point upstream. This means he will be trying to follow the hypotenuse of an imaginary right triangle, and will be doing his 1.1m/sec. along it. 
His rate of progress straight across is therefore sqrt.(1.1^2 - 0.55^2) = 0.95263m/sec. 
Time to cross = (600/0.95263) = 630 secs., or 10.5 mins. 
He needs to point upstream at an angle of arccos (0.55/1.1) = 60 degrees relative to the shoreline.
Hope it helps,please upvote to encourage me.

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