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In a certain inertial frame two light pulses are emitted at point 10 km apart and separated in time 10 ms. An observer moving at a speed V along the line joining these points notes that the pulses are simultaneous. Therefore V is_____(in C).
Correct answer is '0.3'. Can you explain this answer?
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In a certain inertial frame two light pulses are emitted at point 10 k...
Space and time coordinates of two pulses are x1 = 0, t1 = 0 for first pulse
x2 = 10 x 103 m, t2 = 10 x 10-6 sec for second pulse.
For an observer moving with velocity V
Two pulse will be simultaneous. If
x2 = 10 x 103 m, t2 = 10 x 10-6 sec for second pulse.
For an observer moving with velocity V
Two pulse will be simultaneous. If
Most Upvoted Answer
In a certain inertial frame two light pulses are emitted at point 10 k...
Given data:
- Two light pulses are emitted at a distance of 10 km apart.
- The time interval between the two pulses is 10 ms.
- An observer is moving at a speed V along the line connecting the two points.
- The observer notes that the two pulses are simultaneous.
To find:
- The value of V in terms of the speed of light (C).
Solution:
1. Let's consider an inertial frame S in which the two pulses are emitted at the same point (i.e., they are simultaneous).
2. In this frame, the distance between the two pulses (Δx) is 10 km and the time interval between them (Δt) is 10 ms.
3. Using the formula for the speed of light (c = Δx/Δt), we can find the speed of light in this frame:
c = Δx/Δt = 10 km / 10 ms = 1,000,000 m/s
4. Now, let's consider another inertial frame S' in which the observer is moving at a speed V along the line connecting the two points.
5. In this frame, the two pulses are not emitted at the same point (i.e., they are not simultaneous). Instead, the pulse emitted first (pulse 1) will reach the observer before the second pulse (pulse 2).
6. Let's assume that pulse 1 reaches the observer at time t' = 0. Then pulse 2 will reach the observer at time t' = Δt', where Δt' is the time interval between the two pulses in frame S'.
7. Using the formula for time dilation (Δt' = Δt/γ), we can find the time interval between the two pulses in frame S':
Δt' = Δt/γ
where γ is the Lorentz factor given by:
γ = 1/√(1 - v^2/c^2)
8. Since the observer notes that the two pulses are simultaneous in frame S', we have Δt' = 0. Therefore,
0 = Δt/γ
or γ = ∞
9. Substituting this value of γ in the above formula, we get:
∞ = 1/√(1 - v^2/c^2)
or v^2/c^2 = 1 - 1/∞^2
or v^2/c^2 = 1
or v = c
10. Therefore, the speed of the observer relative to the speed of light is V/C = 1.
11. However, we are asked to find the value of V in terms of the speed of light (C). So, we need to convert the above result to that form:
V = c * V/C = c * 1 = c
12. Finally, substituting the value of c in terms of km/s, we get:
V = c = 1,000,000 m/s = 3 * 10^8 m/s = 300,000 km/s
13. Therefore, the value of V in terms of the speed of light (C) is 0.3.
Answer: The value of V in terms of the speed of light (C) is 0.3.
- Two light pulses are emitted at a distance of 10 km apart.
- The time interval between the two pulses is 10 ms.
- An observer is moving at a speed V along the line connecting the two points.
- The observer notes that the two pulses are simultaneous.
To find:
- The value of V in terms of the speed of light (C).
Solution:
1. Let's consider an inertial frame S in which the two pulses are emitted at the same point (i.e., they are simultaneous).
2. In this frame, the distance between the two pulses (Δx) is 10 km and the time interval between them (Δt) is 10 ms.
3. Using the formula for the speed of light (c = Δx/Δt), we can find the speed of light in this frame:
c = Δx/Δt = 10 km / 10 ms = 1,000,000 m/s
4. Now, let's consider another inertial frame S' in which the observer is moving at a speed V along the line connecting the two points.
5. In this frame, the two pulses are not emitted at the same point (i.e., they are not simultaneous). Instead, the pulse emitted first (pulse 1) will reach the observer before the second pulse (pulse 2).
6. Let's assume that pulse 1 reaches the observer at time t' = 0. Then pulse 2 will reach the observer at time t' = Δt', where Δt' is the time interval between the two pulses in frame S'.
7. Using the formula for time dilation (Δt' = Δt/γ), we can find the time interval between the two pulses in frame S':
Δt' = Δt/γ
where γ is the Lorentz factor given by:
γ = 1/√(1 - v^2/c^2)
8. Since the observer notes that the two pulses are simultaneous in frame S', we have Δt' = 0. Therefore,
0 = Δt/γ
or γ = ∞
9. Substituting this value of γ in the above formula, we get:
∞ = 1/√(1 - v^2/c^2)
or v^2/c^2 = 1 - 1/∞^2
or v^2/c^2 = 1
or v = c
10. Therefore, the speed of the observer relative to the speed of light is V/C = 1.
11. However, we are asked to find the value of V in terms of the speed of light (C). So, we need to convert the above result to that form:
V = c * V/C = c * 1 = c
12. Finally, substituting the value of c in terms of km/s, we get:
V = c = 1,000,000 m/s = 3 * 10^8 m/s = 300,000 km/s
13. Therefore, the value of V in terms of the speed of light (C) is 0.3.
Answer: The value of V in terms of the speed of light (C) is 0.3.
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In a certain inertial frame two light pulses are emitted at point 10 km apart and separated in time 10 ms. An observer moving at a speed V along the line joining these points notes that the pulses are simultaneous. Therefore V is_____(in C).Correct answer is '0.3'. Can you explain this answer?
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