Question

A migrating salmon heads in the direction n 45° e, swimming at 2 mi/h relative to the water. the prevailing ocean currents flow due east at 4 mi/h. find the true velocity of the fish as a vector. (assume that the i vector points east, and the j vector points north.)

Answer 1

Calculate for the x and y-components of the velocities involved in this item.

 2 mi/h (45° east)
  x-component = (2 mi/h)(sin 45°)
                     = 1.41 mi/h
  y-component = (2 mil/h)(cos 45°)
                     = 1.41 mi/h

4 mi/h (east)
  x-component = 4 mi/h
  y-component = 0 mi/h

Adding up the corresponding components:
     x-component = 5.4142 mi/h

     y-component = 1.4142 mi/h

Calculating for the resultant,
        R = sqrt ((x²) + (y²))
   
        R = sqrt ((5.4142 mi/h)² + (1.4142 mi/h)²)
             R = 5.60 mi/h

Answer: 5.6 mi/h