On Relative Velocity

Extract

To the observant and intelligent boy or girl who has ever sailed on the Broads or steered a motor-boat in a busy harbour, the ordinary text-book treatment of Relative Velocity must be unsatisfying. The velocity of a ship (or other moving body) P relative to a ship Q is defined as the velocity of P as it “appears” to an observer on Q. But the exact meaning of “appears” is seldom explained. The fact that in all practical applications, observations are being made from one or other of the moving platforms, not from a stationary airship above them, is generally obscured. Thus the relative velocity of P with respect to Q is presented as something mathematical, obtained by the trick of reversing Q's velocity and adding it vectorially to that of P. Now, anyone who has steered a boat and observed another approaching on a converging course, knows that he is not directly concerned with the “actual” velocities (meaning velocities relative to the earth) of either boat. On the other hand, the velocity relative to him of the other boat is a very real thing. But to obtain it he does not have to go through the mental process of imagining that he is going astern when he knows that he is going ahead. All he does is to look over the side and observe. If the other boat's relative bearing does not change, or if its rate of change is small, he knows that it is time to do something with the tiller.