Aboat, 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?

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

r=rho l/a where a is the area, l is the length and rho is resistivity so the greater the area the lesser the resistance thats why the earth pin is thicker bcos current follow the shortest path, so less resistive .