Relativity Problem: Time Dilation and Light Signals in a Rocket Ship

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In summary, the rocket ship leaves Earth at a speed of 3c/5 and when a clock on the rocket says 1 hour has elapsed, it sends a light signal back to Earth. According to Earth clocks, the signal was sent after 1 hour and 15 minutes. According to Earth clocks, the signal arrived back on Earth 2 hours after the rocket left. However, according to the observer on the rocket, the signal arrived back on Earth after 8/5 hours or 1 hour and 36 minutes. The reasoning for the last answer may be incorrect and further clarification is needed.
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Arijit Dutta
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Homework Statement


A rocket ship leaves Earth at a speed of 3c/5. When a clock on the rocket says 1 hour has elapsed, the rocket ship sends a light signal back to earth.

(a) According to Earth clocks, when was the signal sent?
(b) According to Earth clocks, how long after the rocket left did the signal arrive back on earth?
(c) According to the rocket observer, how long after the rocket left did the signal arrive back on earth?

Homework Equations


∆t' = ∆t/ℽ

The Attempt at a Solution


(a)Applying the time dilation eqn. we find that the ans is 1hr 15 min.

(b) Distance traveled by the rocket as seen by the observer on earth= (3c/5)(5/4hr)= 3c/4 hr
Time taken by light to travel this distance = 3/4 hr.
so, total time= 3/4+3/4 = 2hrs.

(c) Applying a similar reasoning wrt rocket we find total time = 1+3/5 = 8/5 hrs.

The last ans seems erroneous. Please correct my reasoning if I'm wrong.
 
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Also,I'm not sure how to approach the first part of the question. Any help would be greatly appreciated. Thanks.
 

FAQ: Relativity Problem: Time Dilation and Light Signals in a Rocket Ship

What is the concept of relativity?

The concept of relativity is a theory in physics that explains how the laws of physics are the same for all observers in uniform motion. It also states that the speed of light in a vacuum is constant for all observers, regardless of their relative motion.

What is a simple relativity problem?

A simple relativity problem is a physics problem that involves applying the principles of relativity to solve a given scenario or situation. These problems often require understanding of concepts like time dilation, length contraction, and the relative motion of objects.

What are some common examples of simple relativity problems?

Some common examples of simple relativity problems include calculating the time dilation experienced by astronauts traveling at high speeds, determining the length contraction of an object moving close to the speed of light, and understanding the twin paradox.

How can one solve a simple relativity problem?

To solve a simple relativity problem, one must first understand the principles of relativity and how they apply to the given situation. Then, using equations and formulas derived from these principles, one can calculate the desired values or variables.

Why is understanding relativity important in science?

Understanding relativity is important in science as it provides a fundamental framework for understanding the behavior of objects in motion and the nature of space and time. It also plays a crucial role in modern physics, particularly in fields such as astrophysics and particle physics.

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