Relative Velocity

It is important to draw a diagram and use a careful labeling process to determine the relative velocity. Each velocity is going to be labeled by two subscripts: the first subscript refers to the object, while the second refers to the reference frame in which the object has this velocity. For example, let's say a boat is crossing a river from one side to the other. We'll use v_BS to represent the Boat's velocity with respect to the Water (this is the velocity that the boat's engine produces against the stream of the river), v_WS to represent the Water's velocity with respect to the Shore (this is the river current), and v_BS to represent the Boat's velocity with respect to the Shore.

If the velocities are along the same line, the relative velocity can be calculated using simple addition and subtraction. However, if they are not on the same line, we must use vector addition.    v_BS = v_BW + v_WS When writing the subscripts this way, it's worth noting that the inner subscripts on the right-hand side (the two W's) are the same, and the outer subscripts on the right-hand side are the same as the subscript shown on the left-hand side. Following this convention, if for example, a fisherman walks with a velocity v_FB relative to the boat, its velocity with respect to the shore is    v_FS = v_FB + v_BW + v_WS