Relativistic Bullet in Space

In summary: The time measured by astronauts at rest with respect to the ship is 60/(.8c - .6c) = 30/c. The time measured by observers moving with the bullet is 100/(.8c - .6c) = 50/c. In summary, the time it takes for the bullet to reach the front of the ship as measured by Earth observers is 80/(.946c -.6c), by astronauts at rest with respect to the ship is 30/c, and by observers moving with the bullet is 50/c.
  • #1
dmayers94
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0

Homework Statement


A rocket of rest length 100 meters is moving at .6c relative to Earth and contains an astronaut at the tail end of the ship. The astronaut fires a bullet toward the front of the ship. The velocity of the bullet relative to the astronaut is 0.8c. How much time does it take the bullet to reach the front of the ship as measured by Earth observers? As measured by astronauts at rest with respect to the ship? As measured by observers moving with the bullet?

Homework Equations


t = t_0*gamma
L = L_0/gamma
time = length/speed

The Attempt at a Solution


There are more parts to this problem that I did not type in because I already solved them, and this gives some extra information that we could use. The bullet is moving .946c relative to Earth observers. The length of the ship according to the astronaut is 100 m, according to Earth observers it is 80 m, and according to observers in the frame of the bullet it is 60 m.

So I know that the time passed is the length of the ship divided by the speed of the bullet relative to the ship, but there are many speeds and multiple lengths of the ship, so I can't figure out which combinations to use. Is the time measured in the Earth frame 80/(.946c -.6c) or can I not simply take the difference of these relativistic speeds? Thanks for any help.
 
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  • #2
dmayers94 said:
Is the time measured in the Earth frame 80/(.946c -.6c)... ?

Yes, that's correct. You can check this result by calculating the time using the Lorentz transformation equations.
 

1. What is a Relativistic Bullet in Space?

A Relativistic Bullet in Space refers to a theoretical concept in which a projectile is accelerated to extremely high speeds, close to the speed of light, through the use of relativistic effects.

2. How is a Relativistic Bullet in Space accelerated?

A Relativistic Bullet in Space can be accelerated through various methods such as electromagnetic fields, particle accelerators, or gravitational slingshots from massive objects.

3. What are the potential applications of a Relativistic Bullet in Space?

A Relativistic Bullet in Space could potentially be used for interstellar travel, as it would allow spacecraft to reach distant destinations in a relatively short amount of time. It could also be used for scientific experiments and studies of relativistic effects.

4. What are the dangers of a Relativistic Bullet in Space?

A Relativistic Bullet in Space could pose a threat to any objects in its path, as it would have an immense amount of kinetic energy. It could also potentially cause damage to the spacecraft itself due to the extreme acceleration forces.

5. Is a Relativistic Bullet in Space possible?

While it is theoretically possible to accelerate an object to relativistic speeds, there are currently no known methods that can achieve this. The technology and engineering required to create a Relativistic Bullet in Space are still beyond our current capabilities.

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