Determine the velocity in a Moving Frame of Reference:

As illustrated in Figure, a ship A moves with a velocity v_A = 40 km/hour whereas ship B moves with a velocity of v_B = 30 km/hour. Determine the velocity of B as it appears to an observer on A.

Solution

Moving axes x, y are fixed to the ship A and all of the vectors are expressed in terms of vectors i, j.

 Then v _A  = 40 i                  and                 v_B  = 30  j

 A point fixed to the x, y axes and coinciding along with the ship A would also move with velocity v_A.

And

and magnitude

                             = 50 km / hour.