A migrating salmon heads in the direction N 45 E swimming at

A migrating salmon heads in the direction N 45° E, swimming at 4 mi/h relative to the water. The prevailing ocean currents flow due east at 3 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.)

Solution

velocity of salmon with respect to current ,V_sc=4cos(90-45)^oi+4sin(90-45)^oj

V_sc=4cos45^oi+4sin45^oj

V_sc=22i+ 22j

velocity of current with respect to ground,V_cg =3i

true velocity of fish,V_sg =velocity of salmon with respect to ground

V_sg =(22i+ 22j)+3i

V_sg =(22 +3)i+ 22j

true velocity of the fish =(22 +3)i+ 22j

true velocity of the fish =5.828i+ 2.828j