Relative Velocities: Speed of C in A's Frame

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In summary, the equation v=[u-v]/[(1-uv)] can be used to determine the speed of train C in the frame of train A, given that trains A and B have equal lengths in the frame of C and train B has a length of 4L/5 in the frame of A. This can be solved by setting u=3/5 and solving for v, resulting in v=10/9. This means that the speed of train C is 10/9 times the speed of train A in the frame of A.
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messier992
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Homework Statement


Three trains A, B, and C with equal proper lengths L are moving on parallel tracks. In the frame of A, B has length 4L/5. In the frame of A, what is the speed of C, if the lengths of A and B are equal in the frame of C

Homework Equations


u'=[u-v]/[(1-uv)]
c=1

The Attempt at a Solution



L' = L/γ => 4L/5 = L*sqrt(1-u^2) => sqrt(1-(4/5)^2) = u => sqrt[(25-16)/25] = u => u= 3/5

Where:
u'=v since is the relative speed of C/B or C/A since B/C=A/C. This is true because L is the same for all trains, and both trains A and B have the same length in C?
v = relative speed of C/A
u = relative speed of B/A

Thus
v=[u-v]/[(1-uv)] => v*(1-uv)=[u-v] => v-v^2*u-u+v=0 => -v^2+(2v/u)-1 = 0 => v^2-(10v/3) +1 = 0
 
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messier992 said:
v=[u-v]/[(1-uv)] => v*(1-uv)=[u-v] => v-v^2*u-u+v=0 => -v^2+(2v/u)-1 = 0 => v^2-(10v/3) +1 = 0
I think this is OK. Did you go on to solve the last equation for v?
 

Related to Relative Velocities: Speed of C in A's Frame

1. What is the concept of relative velocities?

The concept of relative velocities is the measurement of the speed and direction of an object in relation to another object. It takes into account the frame of reference of each object and how their velocities compare to each other.

2. How is the speed of light related to relative velocities?

The speed of light, denoted by "c", is a constant in the theory of relativity and serves as the upper limit for the relative velocities of objects. This means that the speed of light is the fastest speed at which any object can travel.

3. What is the significance of the speed of light in A's frame?

The speed of light in A's frame is significant because it serves as the baseline for measuring relative velocities. This means that the speed of light is always measured as the same value in A's frame, regardless of the velocity of other objects in relation to A.

4. How does the speed of light in A's frame affect the perception of time and space?

As the speed of light is constant in A's frame, it has significant implications on the perception of time and space. This is known as time dilation and length contraction, where time and distance are perceived differently for objects moving at different velocities in relation to A.

5. Can the speed of light in A's frame ever be exceeded?

Based on current scientific understanding, the speed of light in A's frame cannot be exceeded. This is a fundamental principle in the theory of relativity and has been supported by numerous experiments and observations. However, there are still ongoing studies and theories that explore the possibility of faster-than-light travel.

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