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 always remains below the speed of light. Drag the sliders to change the speed of the rocket relative to the ground (indicated by the y-intercept of the solid blue curve) and the speed of the projectile relative to the rocket (indicated by the vertical blue dashed line). The graph shows the relationship between the projectile’s speed in the rocket frame (x-axis) and 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 rocket is stationary, but they diverge more and more the faster the rocket moves.
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