Velocity-addition Formula - Galilean Addition of Velocities

Galilean Addition of Velocities

As Galileo observed, if a ship is moving relative to the shore at velocity v, and a fly is moving with velocity u as measured on the ship, calculating the velocity of the fly as measured on the shore is what is meant by the addition of the velocities v and u. When both the fly and the ship are moving slowly compared to light, it is accurate enough to use the vector sum

\,
\mathbf{s} = \mathbf{v} + \mathbf{u}

where s is the velocity of the fly relative to the shore.

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