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A man can swim at a speed of 3km/hr in still water;he wants to cross a 500m wide river flowing at 2km/hr.He keeps himself always at an angle of 120 with the river flow while swimming.Find the time he will take to cross the river.At what point on the opposite bank will he arrive?

A man can swim at a speed of 3km/hr in still water;he wants to cross a 500m wide river flowing at 2km/hr.He keeps himself always at an angle of 120 with the river flow while swimming.Find the time he will take to cross the river.At what point on the opposite bank will he arrive?

Grade:11

1 Answers

Arun
25763 Points
3 years ago
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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