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A man can swim 3 kmph in still water. He has to cross a 500m wide river flowing at 2 kmph. He keeps himself at an angle of 120' with the river flow while swimming. 

Find the time taken by main in order to cross the river and deterdine the point on the opposite bank he will arrive


Solution

Sum the horizontal components: 3*cos120 + 2 = -1.5 + 2 = 0.5km/h 
His vertical component = 3sin120 = 2.6km/h 
0.500km/2.6 =0.1925hr = 11.6min 
0.5*0.1925 = 0.0962km = 96.2m down stream 
What angle should he swim if he doesn't want to arrive downstream? 
3cosx +2 = 0 -----> cosx = -2/3 -----> x = 131.8 degrees 
How long would it take to cross then? 13.4min 
What if he swam at 90 degrees to the current? 
0.5/3 *60 = 10min but he would be 333m downstream

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