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Unit: Special Relativity Lesson 5: Relativistic Addition of VelocitiesName:___ Date:___Relativistic Addition of Velocities Example #1 Observe the following image. We have a train that is moving to
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How to fill out relativistic velocity addition worked

01
Identify the velocities involved (v and u) that are to be combined.
02
Confirm that they are both relativistic speeds (a significant fraction of the speed of light).
03
Use the relativistic velocity addition formula: \( w = \frac{v + u}{1 + \frac{vu}{c^2}} \), where c is the speed of light.
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Substitute the values of v and u into the formula.
05
Calculate the denominator first (1 + (vu/c^2)).
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Then, calculate the numerator (v + u).
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Divide the numerator by the calculated denominator.
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The result, w, is the resultant velocity in the same frame of reference.

Who needs relativistic velocity addition worked?

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Physicists working in high-speed particle physics.
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Astronomers analyzing velocities of celestial objects moving close to the speed of light.
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Engineers designing systems for high-speed travel or communication in relativistic conditions.
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Students studying advanced physics concepts related to special relativity.
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Relativistic velocity addition is a formula used in the theory of relativity to calculate the resultant velocity of an object when two velocities are combined, taking into account the effects of relativity at speeds close to the speed of light.
Relativistic velocity addition is used by physicists, engineers, and anyone analyzing motion at relativistic speeds, particularly in fields like astrophysics, particle physics, and high-speed dynamics.
To apply relativistic velocity addition, use the formula: v = (u + v') / (1 + (uv'/c^2)), where 'u' is the velocity of one object, 'v'' is the velocity of the other object, 'c' is the speed of light, and 'v' is the resultant velocity.
The purpose of relativistic velocity addition is to accurately determine how fast an object moves when it is observed from a different frame of reference, especially when those velocities are near the speed of light, where classical mechanics fails.
In relativistic velocity addition, it's important to report the initial velocities of the objects, the speed of light, the resultant velocity, and the reference frames from which the measurements are taken.
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