How Does Light Reflect from a Moving Rocket?

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Homework Help Overview

The problem involves a rocket moving towards a mirror at relativistic speeds, specifically 0.90c, and requires determining the time it takes for a light signal to be reflected back to the rocket from the mirror, as measured by both ground observers and those on the rocket. The context is rooted in concepts of special relativity and kinematics.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • The original poster attempts to calculate the time interval for the light signal using a formula but encounters difficulties with the resulting value. Some participants inquire about the specific formula used and whether it pertains to time dilation or Lorentz transformations. There is a discussion about treating the problem similarly to a kinematics scenario while considering relativistic effects.

Discussion Status

Participants are exploring various approaches to the problem, with some suggesting that the first part may not require transformations, while others emphasize the need for careful consideration of distances and speeds in different reference frames. There is no explicit consensus on the best method to use, but guidance has been offered regarding the nature of the problem.

Contextual Notes

There is mention of the challenge posed by the relativistic speeds involved and the need to accurately account for the speed of light in the calculations. The original poster expresses uncertainty about achieving the expected answer, indicating potential gaps in understanding the application of the relevant formulas.

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A rocket approaches a mirror on the ground at a speed of 0.90c. The distance D between the front of the rocket and the mirror is 2.4 * 10^12 m, as measured by ground observers, when a light signal is sent from the front of the rocket. When is the reflected signal received by the rocket as measured by
a) the observers on the ground
b) the observers on the rocket?

I tried for a) working out the time interval using the formula and substituting the values known of speed of rocket and distance of rocket from mirror but I ended up with a huge value. The actual answer is given as 8.42n * 10^3 s and I am unaware how to get to this.
Can anybody give me some help?
 
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any ideas anyone?
 
Which formula is "the formula"? Are you talking about a time dilation formula or a Lorentz transformation? I assume that the light signal is actually traveling at the speed of light. The problem is much like any kinematics problem if you can find all the necessary information in each frame. Basically, you have the rocket's velocity, and you want to know how fast it is going according to the ground. When working part b, watch your distance.
 
i was talking about the time dilation formulca, is this the right one to use?
 
i was talking about the time dilation formulca, is this the right one to use?
 
The first part you actually don't need to do any transformations, if I am reading it right, since all the information given to you is with reference to the ground. Is this the part you got wrong?

Think of it like a regular kinematics problem because the only difference is that the numbers are bigger, but the algebra is the same. It is almost the same as some guy skateboarding, throwing a ball at a wall, and then catching it. Just remember that the light out of the spaceship can't exceed the speed of light!

The second part you will need more than just time dilation.
 

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