Question

A man can swim at a speed of 3 km/h in still water. He wants to cross a 500 m wide river flowing at 2 km/h. He keeps himself at an angle of 120° with the river flow while swimming.

(a) Find the time he takes to cross the river.

(b) At what point on the opposite bank will he arrive?

Answer 1

given, 

speed of man, Vm = 3km/hr

speed of river, Vr = 2km/hr

angle which the man makes with the direction of motion of river = 120

The resultant velocity of man can be calculated by the parallelogram law of vectors as,

angle between Vr and VR

now time required to cross the river = OB/VR

in trianle ABO, angleAOB = 90o - 79o = 11o

so, OB = AO/cos11o =  0.5/0.981 = 0.509

so time required = 0.509/2.6 = 0.196hr = 0.196x60x60 = 705.6s

 

Now the point  where he will reach is B, and the distance of  B from A = AB = AOtan11 =  0.097km 

                                                                                                                                          = 0.097x1000= 97m