I need help on question 12. 12.Scientists in one lab observe that two sparks occur in the same place 4.0 secondsapart in time. In another lab that is moving relative to the first, observations record two sparksthat occur 5.0 seconds apart and separated by a distance of 3.0 seconds (or 9.0 × 108 m). Useeither the spacetime interval or the Lorentz factor to check whether these measurements couldbe measurements of the same two sparks. Be sure to explain how your calculations relate tothe question!

key conceptspacetime interval of two events is same for all inertial frame Thank you

Answered: 12. Scientists in one lab observe that…

Physics for Scientists and Engineers

10th Edition

ISBN:9781337553278

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter38: Relativity

Section: Chapter Questions

Problem 4P: A muon formed high in the Earths atmosphere is measured by an observer on the Earths surface to...

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(a) All but the closest galaxies are receding from our own Milky Way Galaxy. If a galaxy 12.0109ly ly away is receding from us at 0. 0.900c, at what velocity relative to us must we send an exploratory probe to approach the other galaxy at 0.990c, as measured from that galaxy? (b) How long will it take the probe to reach the other galaxy as measured from the Earth? You may assume that the velocity of the other galaxy remains constant. (c) How long will it then take for a radio signal to be beamed back? (All of this is possible in principle, but not practical.)
A pulsar is a stellar object that emits light in short bursts. Suppose a pulsar with a speed of 0.950c approaches Earth, and a rocket with a speed of 0.995c heads toward the pulsar. (Both speeds are measured in Earth's frame of reference.) If the pulsar emits 10.0 pulses per second in its own frame of reference, at what rate are the pulses emitted in the rockets frame of reference?
(a) Find the kinetic energy of a 78.0-kg spacecraft launched out of the solar system with speed 106 km/s by using the classical equation K=12mu2. (b) What If? Calculate its kinetic energy using the relativistic equation. (c) Explain the result of comparing the answers of parts (a) and (b).
(a) Suppose the speed of light were only 3000 m/s. A jet fighter moving toward a target on the ground at 800 m/s shoots bullets, each having a muzzle velocity of 1000 m/s. What are the bullets' velocity relative to the target? (b) If the speed of light was this small, would you observe relativistic effects in everyday life? Discuss.
Suppose our Sun is about to explode. In an effort to escape, we depart in a spacecraft at v = 0.800c and head toward the star Tau Ceti, 12.0 ly away. When we reach the midpoint of our journey from the Earth, we see our Sun explode, and, unfortunately, at the same instant, we see Tau Ceti explode as well. (a) In the spacecrafts frame of reference, should we conclude that the two explosions occurred simultaneously? If not, which occurred first? (b) What If? In a frame of reference in which the Sun and Tau Ceti are at rest, did they explode simultaneously? If not, which exploded first?
An alien spaceship traveling at 0.600c toward the Earth launches a landing craft. The landing craft travels in the same direction with a speed of 0.800r relative to the mother ship. As measured on the Earth, the spaceship is 0.200 ly from the Earth when the landing craft is launched, (a) What speed do the Earth-based observers measure for the approaching landing craft? What is the distance to the Earth at the moment of the landing craft's launch as measured by the aliens? What travel time is required for the landing craft to reach the Earth as measured by the aliens on the mother ship? (d) If' the landing craft has a mass of 4.00 10s kg. what is its kinetic energy as measured in the Earth reference frame?
Suppose an astronaut is moving relative to the Earth at a significant fraction of the speed of light. (a) Does he observe the rate of his clocks to have slowed? (b) What change in the rate of Earth-bound clocks does he see? (c) Does his ship seem to him to shorten? (d) What about the distance between stars that lie on lines parallel to his motion? (e) Do he and an Earth-bound observer agree on his velocity relative to the Earth?
. If the relativistic kinetic energy of a particle is 9 times its rest energy, at what fraction of the speed of light must the particle be traveling?
A muon formed high in the Earths atmosphere is measured by an observer on the Earths surface to travel at speed = 0.990c for a distance of 4.60 km before it decays into an electron, a neutrino, and an antineutrino (c+v+v). (a) For what time interval does the muon live as measured in its reference frame? (b) How far does the Earth travel as measured in the frame of the muon?
(a) How fast would an athlete need to be running for a 100-m race to look 100 yd long? (b) Is the answer consistent with the fact that relativistic effects are difficult to observe in ordinary circumstances? Explain.
An interstellar space probe is launched from Earth. After a brief period of acceleration, it moves with a constant velocity, 70.0% of the speed of light. Its nuclear-powered batteries supply the energy to keep its data transmitter active continuously. The batteries have a lifetime of 15.0 years as measured in a rest frame. (a) How long do the batteries on the space probe last as measured by mission control on Earth? (b) How far is the probe from Earth when its batteries fail as measured by mission control? (c) How far is the probe from Earth as measured by its built-in trip odometer when its batteries fail? (d) For what total time after launch are data received from the probe by mission control? Note dial radio waves travel at the speed of light and fill the space between the probe and Earth at the time the battery fails.
A muon has a rest mass energy of 105.7 MeV, and it decays into an electron and a massless particle. (a) If all the lost mass is converted into the electron's kinetic energy, find for the electron. (b) What is the electron's velocity?

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