When and Where Will Spaceships #1 and #2 Meet in Special Relativity?

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In summary, two spaceships, one moving at a velocity of 0.2c and the other at 0.6c, are 3 x 10^9 m apart in reference frame S. The problem asks for the time and position at which the faster spaceship will catch up with the slower one in both frame S and the reference frame of the slower spaceship. The relative velocity between the two spaceships in the reference frame of the slower one is calculated to be 0.7143c, but this information is not useful for solving the problem. Instead, the catch up time and position can be found using classical methods in frame S, and then the Lorentz transform can be used to determine the time in the reference frame
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SMG75
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Spaceships--special relativity

Homework Statement


Spaceship #1 moves with a velocity of .2c in the positive x direction of reference frame S. Spaceship #2, moving in the same direction with a speed of .6c is 3 x 10^9 m behind. At what times in reference frames S, and in the reference frame of ship #1, will 2 catch up with 1.


Homework Equations





The Attempt at a Solution


I solved for the relative velocity of ship 2 in the IRF of ship 1. I got .7143c. I'm not really sure where to proceed from here. Any ideas?
 
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  • #2


The spaceships move in the same direction, so the relative velocity can't be larger than 0.6c. I don't think it's very useful to compute anyway.

Just compute when and where the spaceships catch up in frame S. This can be done in the classical way. Then use the lorentz transform to find the time in the frame of
ship #1
 

FAQ: When and Where Will Spaceships #1 and #2 Meet in Special Relativity?

What is special relativity and how does it relate to spaceships?

Special relativity is a theory developed by Albert Einstein that describes the relationship between space and time for objects moving at high speeds. It explains how the laws of physics are the same for all observers, regardless of their relative motion. This theory is particularly important for spaceships because they often travel at speeds close to the speed of light, where the effects of special relativity become significant.

How does special relativity affect the time on a spaceship?

According to special relativity, time can appear to pass differently for two observers in different reference frames. For a person on a spaceship traveling at high speeds, time will appear to pass slower compared to someone on Earth. This effect, known as time dilation, becomes more significant as the speed of the spaceship approaches the speed of light.

Can spaceships travel faster than the speed of light?

According to special relativity, the speed of light is an absolute speed limit and cannot be exceeded. This means that it is not possible for a spaceship to travel faster than the speed of light. As the spaceship approaches the speed of light, its mass would increase infinitely and it would require an infinite amount of energy to accelerate further.

How does special relativity affect distances in space?

Another effect of special relativity is length contraction, which states that an object's length will appear shorter to an observer who is moving relative to it. This means that distances in space can appear shorter for someone on a spaceship traveling at high speeds compared to someone on Earth. However, this effect is only noticeable at speeds close to the speed of light.

How does special relativity explain the twin paradox?

The twin paradox is a thought experiment that demonstrates the effects of time dilation in special relativity. It involves one twin staying on Earth while the other twin travels through space at high speeds. When the traveling twin returns to Earth, they will have aged slower than the twin who stayed on Earth. This is because time passed slower for the traveling twin due to their high speed, demonstrating the effects of special relativity on the passage of time.

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