Water from a vertical pipe emerges as a 10-cm-diameter cylinder and falls straight down 7.5 m into a bucket. The water exits the pipe with a speed of 2.0 m/s. What is the diameter of the column of water as it hits the bucke g

In this item, we take the direction of the bird, given to be north, to be the positive side. In the opposite is the direction of the air (south), we take as negative. The vectors are now,
   + 11 (bird) and -2 (air)

The sum of he vectors is equal to the sum of the two numbers. That is equal to +9. Thus, the magnitude is equal to 9 and the direction is +.