A river 675-m wide is flowing East at a uniform speed of 2.20 m s^-1. A student

Question

A river 675-m wide is flowing East at a uniform speed of 2.20 m s^-1. A student has a boat, which sails at 3.20 m s^-1 in still water. The student wants to sail directly across the river from South to North (i.e. perpendicular to the banks of the riser) In what direction must the student point the boat? What time will it take to cross the river? A fish is swimming upstream (i.e. to the West) at 3.00 ms^-1 relative to the water. Calculate the magnitude of the velocity of the fish as seen by the student as the student is sailing across the river.

Explanation / Answer

a) Here, 2.20 = 3.20 * cos(theta)

=> theta = 46.56 degree

Thus, direction must student point boat = 180 - 46.56

                                                                  = 133.44 degree   from East anticlockwise

b) time it will take = 675/2.323

                               = 290.57 sec

c) magnitude of velocity of fish = sqrt(0.82 + 3.22 + 2 * 0.8 * 3.2 * cos46.56)

                                                   = 3.794 m/s

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