Relativistic particles speed through the atmosphere of the Earth at 0.6c. If the upper atmosphere is 500 km from the ground, from the perspective of an observer on Earth, how long does it take the particles to travel that distance? What equation do I use to solve this this?
I am grateful for your answer but we are learning that particules and we are looking how an observer on the side would see it. We learned about time dillatation and its equations. I am just not sure how to use the time dillation equation to find how long it take to travel that distance since I dont have the velocity.
Relativistic particles speed through the atmosphere of the Earth at 0.6c. If the upper atmosphere is 500 km from the ground, from the perspective of an observer on Earth, how long does it take the particles to travel that distance? What equation do I use to solve this this?
Since the speed of light, in a vacuum, is 299,792,458m/s, then it follows that light can travel 500Km X 1,000m=500,000m in 500,000/299,792,458=1/600 of 1 second. Of course, in reality it takes a little longer that because of the effects of the atmosphere on the particle in question. Also, relativistic effects are NOT taken into account because it complicates things.
Sorry, First I neglected to take the speed of the particle into account. Since it's .6c, then that means 299,792,458 X .6=179,875,474.8m . Then 500,000/179,875,474.8=1/360 of 1 second. What formula do you have in mind?. There are different formulas for slowing of moving clocks, moving bodies becoming more massive, shortening of bodies in the direction of motion.....etc.
I am grateful for your answer but we are learning that particules and we are looking how an observer on the side would see it. We learned about time dillatation and its equations. I am just not sure how to use the time dillation equation to find how long it take to travel that distance since I dont have the velocity.
There is a simple formula for time dilation, which is a follows: Td=1 / sqrt(1 - v^2). v is in terms of c.
For example: if a particle travel at v=.9c, then =1/ sqrt(1-.9^2)=1/sqrt(.19)=1/0.43589=2.3, so
Td=2.3. That's if a particle(or a spacecraft for that matter), travels at 90% of the speed of light, time slows down by factor of about 2.3 times of clocks at rest. So, this means that if you travelled in a spacecraft at 90% of the speed of light, for every 2.3 years that passed on earth, only one year would have passed on the spaceship.
