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Velocities cannot add to greater than the speed of light, provided that v is less than c and $u\prime $ does not exceed c . The following example illustrates that relativistic velocity addition is not as symmetric as classical velocity addition.
Check Your Understanding Distances along a direction perpendicular to the relative motion of the two frames are the same in both frames. Why then are velocities perpendicular to the x -direction different in the two frames?
Although displacements perpendicular to the relative motion are the same in both frames of reference, the time interval between events differ, and differences in dt and $dt\prime $ lead to different velocities seen from the two frames.
If two spaceships are heading directly toward each other at 0.800 c , at what speed must a canister be shot from the first ship to approach the other at 0.999 c as seen by the second ship?
Two planets are on a collision course, heading directly toward each other at 0.250 c . A spaceship sent from one planet approaches the second at 0.750 c as seen by the second planet. What is the velocity of the ship relative to the first planet?
0.615 c
When a missile is shot from one spaceship toward another, it leaves the first at 0.950 c and approaches the other at 0.750 c . What is the relative velocity of the two ships?
What is the relative velocity of two spaceships if one fires a missile at the other at 0.750 c and the other observes it to approach at 0.950 c ?
0.696 c
Prove that for any relative velocity v between two observers, a beam of light sent from one to the other will approach at speed c (provided that v is less than c , of course).
Show that for any relative velocity v between two observers, a beam of light projected by one directly away from the other will move away at the speed of light (provided that v is less than c , of course).
(Proof)
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