Special relativity, relative velocities

In summary, the problem involves two rockets, A and B, with relative velocities of 0.5c and 0.8c, respectively, to an Earth based observer. The question is asking for the speed at which rocket B appears to catch up to rocket A from the perspective of the Earth based observer. This can be solved using the given equation, which relates a particle's velocity in one frame to its velocity in another frame, with the same frame being used for the entire equation. In this case, the frame used is rocket A's frame since it appears in both measurements.
  • #1
C.E
102
0
1. Hi, could somebody please help me to answer the following Relativity question?
Rocket A is traveling at 0.5c relative to an Earth based observer and Rocket B travels at 0.8c Relative to rocket A. At what speed does rocket B appear to catch rocket A to an Earth based observer?


2. We are given that for 1 dimensional motion a particles velocity vx in the frame S is related to its velocity vx' in the frame S' (which is moving with velocity u relative to frame S) by
vx=vx'+u/(1+uvx'/c^2).

3.Can somebody please explain how to tackle this kind of question? I keep getting really confused (particularly about what is in which reference frame) and don't even know how to start. (By the way this is not assesed work merely revision so feel free to give as much help as you deem appropriate).
 
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  • #2
C.E said:
Rocket A is traveling at 0.5c relative to an Earth based observer and Rocket B travels at 0.8c Relative to rocket A. At what speed does rocket B appear to catch rocket A to an Earth based observer?

Hi C.E! :smile:

You just use the equation they give you …
We are given that for 1 dimensional motion a particles velocity vx in the frame S is related to its velocity vx' in the frame S' (which is moving with velocity u relative to frame S) by
vx=vx'+u/(1+uvx'/c^2).

but you must use the same frame for the whole equation (!), so in this case, that would be A's frame (because A appears in both measurements) …

so that will give you B's velocity relative to Earth :wink:
 

1. What is special relativity?

Special relativity is a theory developed by Albert Einstein that explains how objects move in relation to one another at high speeds. It states that the laws of physics are the same for all observers moving at constant velocities, and that the speed of light is the same for all observers, regardless of their relative motion.

2. How does special relativity affect relative velocities?

Special relativity predicts that the relative velocities between objects moving at high speeds will be different from what we observe at lower speeds. This is due to the time dilation and length contraction effects, which cause objects to appear to move slower and shorter in the direction of their motion.

3. Can special relativity be applied to everyday situations?

Yes, special relativity can be applied to everyday situations, although the effects are negligible at low speeds. For example, GPS systems use special relativity calculations to accurately determine location and time, as the satellites are moving at high speeds relative to Earth.

4. How does special relativity explain the concept of time dilation?

Time dilation is a phenomenon predicted by special relativity that states time passes slower for objects moving at high speeds. This is due to the fact that as an object's speed increases, its relative time slows down, resulting in a difference in time between two observers moving at different speeds.

5. What is the difference between special relativity and general relativity?

Special relativity deals with the laws of physics in inertial frames of reference, while general relativity extends these laws to include non-inertial frames of reference. General relativity also takes into account the effects of gravity, while special relativity does not.

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