Relativity, how it affects observation.

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Relativity significantly alters observations of length, time, and mass depending on the observer's frame of reference. A spaceship traveling at 80% the speed of light appears shorter to a stationary observer, measuring 39m, while an astronaut inside measures it as 65m. For a journey to Proxima Centauri at 50% the speed of light, the astronaut experiences approximately 7.45 years, while an Earth observer measures about 8.6 years. An astronaut with a mass of 75 kg will be perceived as approximately 113 kg by a stationary observer due to relativistic effects. Understanding these concepts is crucial for grasping the implications of relativity on observation.
chewtoy929
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I'm having a bit of trouble understanding relativity, and would like some help with the following problems:
1. A spaceship passes a stationary observer at a speed that is 80% the speed of light. At rest, this ship is 65m long. What does the observer say about the length of the spaceship? How does this length compare to that
measured by an astronaut inside the spaceship?

2. A spaceship capable of flying 50% of the speed of light, travels from Earth to Proxima Centauri, the star closest to the Earth other than our own Sun at a distance of 4.3 light years. What does an astronaut inside the spaceship have to say about the length of time it takes to reach Proxima Centauri? How does this time compare to that measured by an observer stationed on Earth?

3. On Earth an astronaut has a mass of 75 kg. If they are in a spaceship that is flying at 75% of the speed of light, then what does a stationary observer have to say about the astronaut's mass? What does the astronaut have to say about their own mass?
 
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Why don't you start out with the concepts behind each problem; what will be the general answer to each. Then, what relevant equations do you think you might need?
 
1= 65m from astronaut, 39 observer
2= 7.447818 astronaut, 8.6 observer
3= 75 kg astronaut, ~113 kg observer
 
Looks good!

It sounded like you were having trouble with some of the concepts, however. Are they clear now?
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...

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