Question

A boat, whose speed in still water is 2.50 m/s, must cross a 285-m wide river and arrive at a point 118m upstream from where it starts. To do so, the pilot must head the boat at a 45.0 degrees upstream angle. What is the speed of the rivers current?

Answer 1

The figure shows the arrangement of system

The velocity of boat can be resolved in to two

     Horizontal component  = vcos θ = 2.50 cos 45 = 1.768 m/s

     Vertical component  = vsin θ = 2.50 sin 45 = 1.768 m/s

   Due to horizontal component the boat arrive arrives upstream,

           Total horizontal velocity =  1.768 - Vr, where Vr is the velocity of river.

  Total time taken to cross the river = width of river/ Vertical component of velocity

                         t = 285/1.768 = 161.20 seconds

So 118 meter is traveled at a velocity of 1.768-Vr in 161.20 seconds

That is           118 = (1.768-Vr)*161.20

                     1.768 - Vr =0.732

                         Vr = 1.036 m/s

So velocity of river flow =1.036 m/s