A muon travels through the atmosphere at a speed of . According to the muon, how thick is the atmosphere?
The atmosphere is thick.
We have given that, a muon travels through the atmosphere at a speed of .
The correct length of the atmosphere in this scenario is .
For length contraction, use the following formula:
Therefore, according to the muon, the atmosphere is thick.
A starship voyages to a distant planet away. The explorers stay 1 year, return at the same speed, and arrive back on earth , as measured on earth after they left. Assume that the time needed to accelerate and decelerate is negligible.
a. What is the speed of the starship?
b. How much time has elapsed on the astronauts’ chronometers?
In an attempt to reduce the extraordinarily long travel times for voyaging to distant stars, some people have suggested traveling at close to the speed of light. Suppose you wish to visit the red giant star Betelgeuse, which is away, and that you want your rocket to move so fast that you age only during the round trip.
a . How fast, as a fraction of c, must the rocket travel relative to earth?
b. How much energy is needed to accelerate the rocket to this speed?
c. Compare this amount of energy to the total energy used by the United States in the year , which was roughly
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