Check out the interactive demonstration below, which shows how velocities are added relativistically. Unlike Galilean relativity, special relativity predicts that the observed speed of the projectile in the ground frame must always remain below the speed of light. Drag the sliders to change the speed of the rocket relative to the ground (indicated by the vertical blue dashed line) and the speed of the projectile relative to the rocket (indicated by the y-intercept of the solid blue curve). (This demo is very similar to the previous demo; the difference is that the roles of the two sliders are interchanged in the graph.) The graph shows the relationship between the rocket’s speed in the ground frame (x-axis) and the projectile’s speed in the ground frame (y-axis). The solid blue curve depicts the Einsteinian prediction whereas the dashed gray curve depicts the Galilean prediction. Notice how the two curves overlap when the projectile is stationary, but they diverge more and more the faster the projectile moves.
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