[justify]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.[br][br]For example, let's say a boat is crossing a river from one side to the other. We'll use [b]v[/b][sub]BS[/sub] to represent the [b]B[/b]oat's velocity with respect to the [b]W[/b]ater [i](this is the velocity that the boat's engine produces against the stream of the river)[/i], [b]v[/b][sub]WS[/sub] to represent the [b]W[/b]ater's velocity with respect to the [b]S[/b]hore [i](this is the river current)[/i], and [b]v[/b][sub]BS[/sub] to represent the [b]B[/b]oat's velocity with respect to the [b]S[/b]hore.[/justify]

[justify][/justify][justify][/justify][right][/right][justify][/justify][center][/center][justify][/justify][justify]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.[br][b][br]    v[/b][sub]BS [/sub]= [b]v[/b][sub]BW[/sub] + [b]v[/b][sub]WS[br][br][/sub]When writing the subscripts this way, it's worth noting that the inner subscripts on the right-hand side [i](the two W's)[/i] are the same, and the outer subscripts on the right-hand side are the same as the subscript shown on the left-hand side.[br][br]Following this convention, if for example, a fisherman walks with a velocity [b]v[/b][sub]FB[/sub] relative to the boat, its velocity with respect to the shore is[br][br][b]    v[/b][sub]FS [/sub]= [b]v[/b][sub]FB[/sub] + [b]v[/b][sub]BW [/sub]+ [b]v[/b][sub]WS[/sub][/justify]