Trout are swimming up the Blackfoot River at forty meters per hour (relative to an observer on the bank of the river) to spawn, and their density is four fish per meter cubed. John, and his sons Norman and Paul, love to fish along the Blackfoot River. The river runs parallel to the x-axis, its surface is parallel to the plane z = 0, and the net they are using has a rectangular opening that is one half meter wide by one half meter long with normal vector n. While they all put the net into the river so that n j = 0, each member of the family has their own special technique for using the net. Advice: Draw pictures - this is a problem about visualizing what is happening, it is not a problem about using math in clever ways.

(a) John puts the net into the river so that its opening is perpendicular to the surface of the water (that is, n k = 0), approximately how many fish does John catch in ten minutes?

(b) Norman puts the net into the river so that its opening is parallel to the surface of the water (that is, n k = .25 meters squared), approximately how many fish does Norman catch in ten minutes?

(c) Paul puts the net into the river so that its opening is at an angle of thirty degrees to the surface of the water, approximately how many fish does Paul catch in ten minutes?