Question

Modern Physics

Problem 1 A what is the average distan stubatomic particle has a lifetime of 2.2 lus. If the particle is moving 0.9c erage litetime measured by the laboratory reference frame? What is the ce traveled by the particle, that the laboratory measures, before it decays? life Problem 2 in the movie intersteęllar it is said that the Endurance traveled from Barth t. Pinst try km/s and then fr hink about what trajectory orbit the Sun. From distance and how that time might different from the people on the plane om Mars to Saturn at 21 km/s on a mission to save the planet. First try to they might have taken and justify it based on how the planets there think about how much time it would take for them to travel that 1. Problem 3 A NASA scientist observes an alien spacecraft is flying through space past the earth while looking at the moon. A safety light is seen blinking, where it is measured to periodically stay on and off for 0.19 s. The NASA scientist spent time at area 51 and knows that the alien ship's standard safety light blinks at a on off rate of 83.33 Hz. What is the speed of the spacecraft relative to the earth? Explain. 2

Answer 1

Solution for problem 1..

After Einstein gave his theory of special relativity, our understanding of the nature of space and time was drastically shifted. Earlier in Newtonian framework time was absolute and it flowed uniformly no matter what frame we are in. But now we know it's not the Case in reality. The flow of time is not same in all frames, it depends upon which frame we are in. Now when we say a subatomic particle has a lifetime of 2.2 microseconds, what we mean that before the particles decays it experiences that much time in its rest frame. We call it the proper time. Now an observer in the laboratory frame will surely disagree with the amount of decay time his or her clock measures, as the particle is moving relative to the laboratory frame and hence in that frame the Clock carried by the particle will appear to slowed down. We can find out how much time the laboratory clock measures before the particle dacays using Lorentz Transformation..See the calculations in following picture..