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An observer O at rest midway between 2 sources of light at x = 0 and x = 10m, observes the 2 sources to flash simultaneously. According to a second observer O', moving at a constant speed parallel to the x-axis, one source flashes 13ns before the other. Find the speed of O' relatives to O (in units of c)
Correct answer is '0.363'. Can you explain this answer?
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Verified Answer
An observerOat rest midway between 2 sources of light atx= 0 andx= 10m...
A → Flashing observed from first source (at x = 0)
B → Flashing observed from second source (at x = 10)
Now Event (A) occurs (at x = 0) Event B occurs (at x = 10)
For O t = 0 t = 0
For O' t = 0 t = 13 ns
For O' t = 0 t = 13 ns
Here we assumed that both observers observe event A at t = 0
Now the problem says that for O', one event occurs 13 ns before the other.
∴ O' observes event B at t = 13 ns
Now, applying transformation for time
∴ O' observes event B at t = 13 ns
Now, applying transformation for time
The correct answer is: 0.363
Most Upvoted Answer
An observerOat rest midway between 2 sources of light atx= 0 andx= 10m...
Given information:
- Observer O is at rest midway between two sources of light at x=0 and x=10m.
- Observer O observes the two sources flashing simultaneously.
- Observer O' is moving at a constant speed parallel to the x-axis.
- According to observer O', one source flashes 13ns before the other.
To find:
The speed of observer O' relative to O in units of c.
Approach:
1. Determine the time difference observed by observer O'.
2. Use the time difference and the distance between the sources to find the speed of observer O' relative to O.
Solution:
Step 1: Determine the time difference observed by observer O':
- Let's assume that the observer O is at the origin and the two sources are at x=0 and x=10m.
- Since the sources flash simultaneously for observer O, the light from the source at x=0 will take time t1 to reach observer O and the light from the source at x=10m will take time t2 to reach observer O.
- According to observer O', one source flashes 13ns before the other.
- Let's assume that the source at x=0 flashes first. Therefore, t1 = t2 + 13ns.
Step 2: Use the time difference and the distance between the sources to find the speed of observer O' relative to O:
- The time taken by light to travel a distance d is given by the formula: t = d/c, where c is the speed of light.
- Therefore, t1 = 0/c and t2 = 10/c.
- Substituting these values in the equation t1 = t2 + 13ns, we get 0/c = 10/c + 13ns.
- Rearranging the equation, we get 10/c = 13ns.
- Solving for c, we get c = 10/13ns.
Step 3: Convert the speed of observer O' relative to O to units of c:
- The speed of observer O' relative to O is given by the formula: v = d/t2, where d is the distance between the sources and t2 is the time taken by light to travel this distance.
- Substituting the values, we get v = 10/10/c = c.
Final Answer:
The speed of observer O' relative to O is 1, which is equivalent to c.
- Observer O is at rest midway between two sources of light at x=0 and x=10m.
- Observer O observes the two sources flashing simultaneously.
- Observer O' is moving at a constant speed parallel to the x-axis.
- According to observer O', one source flashes 13ns before the other.
To find:
The speed of observer O' relative to O in units of c.
Approach:
1. Determine the time difference observed by observer O'.
2. Use the time difference and the distance between the sources to find the speed of observer O' relative to O.
Solution:
Step 1: Determine the time difference observed by observer O':
- Let's assume that the observer O is at the origin and the two sources are at x=0 and x=10m.
- Since the sources flash simultaneously for observer O, the light from the source at x=0 will take time t1 to reach observer O and the light from the source at x=10m will take time t2 to reach observer O.
- According to observer O', one source flashes 13ns before the other.
- Let's assume that the source at x=0 flashes first. Therefore, t1 = t2 + 13ns.
Step 2: Use the time difference and the distance between the sources to find the speed of observer O' relative to O:
- The time taken by light to travel a distance d is given by the formula: t = d/c, where c is the speed of light.
- Therefore, t1 = 0/c and t2 = 10/c.
- Substituting these values in the equation t1 = t2 + 13ns, we get 0/c = 10/c + 13ns.
- Rearranging the equation, we get 10/c = 13ns.
- Solving for c, we get c = 10/13ns.
Step 3: Convert the speed of observer O' relative to O to units of c:
- The speed of observer O' relative to O is given by the formula: v = d/t2, where d is the distance between the sources and t2 is the time taken by light to travel this distance.
- Substituting the values, we get v = 10/10/c = c.
Final Answer:
The speed of observer O' relative to O is 1, which is equivalent to c.
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An observerOat rest midway between 2 sources of light atx= 0 andx= 10m, observes the 2 sources to flash simultaneously. According to a second observerO', moving at a constant speed parallel to thex-axis, one source flashes 13nsbefore the other. Find the speed ofO'relatives toO(in units ofc)Correct answer is '0.363'. Can you explain this answer?
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An observerOat rest midway between 2 sources of light atx= 0 andx= 10m, observes the 2 sources to flash simultaneously. According to a second observerO', moving at a constant speed parallel to thex-axis, one source flashes 13nsbefore the other. Find the speed ofO'relatives toO(in units ofc)Correct answer is '0.363'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about An observerOat rest midway between 2 sources of light atx= 0 andx= 10m, observes the 2 sources to flash simultaneously. According to a second observerO', moving at a constant speed parallel to thex-axis, one source flashes 13nsbefore the other. Find the speed ofO'relatives toO(in units ofc)Correct answer is '0.363'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An observerOat rest midway between 2 sources of light atx= 0 andx= 10m, observes the 2 sources to flash simultaneously. According to a second observerO', moving at a constant speed parallel to thex-axis, one source flashes 13nsbefore the other. Find the speed ofO'relatives toO(in units ofc)Correct answer is '0.363'. Can you explain this answer?.
An observerOat rest midway between 2 sources of light atx= 0 andx= 10m, observes the 2 sources to flash simultaneously. According to a second observerO', moving at a constant speed parallel to thex-axis, one source flashes 13nsbefore the other. Find the speed ofO'relatives toO(in units ofc)Correct answer is '0.363'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about An observerOat rest midway between 2 sources of light atx= 0 andx= 10m, observes the 2 sources to flash simultaneously. According to a second observerO', moving at a constant speed parallel to thex-axis, one source flashes 13nsbefore the other. Find the speed ofO'relatives toO(in units ofc)Correct answer is '0.363'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An observerOat rest midway between 2 sources of light atx= 0 andx= 10m, observes the 2 sources to flash simultaneously. According to a second observerO', moving at a constant speed parallel to thex-axis, one source flashes 13nsbefore the other. Find the speed ofO'relatives toO(in units ofc)Correct answer is '0.363'. Can you explain this answer?.
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