General Physics, 2nd Edition
2nd Edition
ISBN: 9780471522782
Author: Morton M. Sternheim
Publisher: WILEY
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Chapter 25, Problem 1E
To determine
Speed of ground as seen by pilot.
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A beam of light is moving directly along the spaceship, but through an
old-fashioned fiber optic cable. The speed of light in the cable is 0.6 times the
speed of light in a vacuum. The spaceship is moving at 0.8 times the speed of
light. What speed do you observe from the ground?
You have an assistantship with a math professor in a future world where space travel is common and spacecraft regularly achieve near-light speeds. A spacecraft has taken off recently to carry individuals to colonize an Earth-like planet around a nearby star. Your professor, who remains on Earth,is teaching the students on the spacecraft via the future version of distance learning. It is time for the students on the spacecraft to take a math exam. The professor wishes the students to have a time interval Δtp = 2.00 h to complete the exam, so just as the spacecraft passes Earth on its last triparound the Sun at its constant cruising speed of 0.960c, she sends a signal to the proctor to have the students begin the exam. Knowing of your experience in physics courses, the professor asks you to determine the time interval through which she should wait before sending a radio signal to thedeparting spacecraft to tell the proctor to have the students stop working on the exam.
Consider the case of two kids, Sam and Peter, riding a train and playing catch in an empty car. The train is moving to the right at 10 m/s. The kids can throw the ball at a speed of 5 m/s. The side of the car is transparent and a poodle named Max can see the boys playing inside.
What is the speed and direction of Sam’s throw to Peter, according to Max? Explain.
Chapter 25 Solutions
General Physics, 2nd Edition
Ch. 25 - Prob. 1RQCh. 25 - Prob. 2RQCh. 25 - Prob. 3RQCh. 25 - Prob. 4RQCh. 25 - Prob. 5RQCh. 25 - Prob. 6RQCh. 25 - Prob. 7RQCh. 25 - Prob. 8RQCh. 25 - Prob. 9RQCh. 25 - Prob. 1E
Ch. 25 - Prob. 2ECh. 25 - Prob. 3ECh. 25 - Prob. 4ECh. 25 - Prob. 5ECh. 25 - Prob. 6ECh. 25 - Prob. 7ECh. 25 - Prob. 8ECh. 25 - Prob. 9ECh. 25 - Prob. 10ECh. 25 - Prob. 11ECh. 25 - Prob. 12ECh. 25 - Prob. 13ECh. 25 - Prob. 14ECh. 25 - Prob. 15ECh. 25 - Prob. 16ECh. 25 - Prob. 17ECh. 25 - Prob. 18ECh. 25 - Prob. 19ECh. 25 - Prob. 20ECh. 25 - Prob. 21ECh. 25 - Prob. 22ECh. 25 - Prob. 23ECh. 25 - Prob. 24ECh. 25 - Prob. 25ECh. 25 - Prob. 26ECh. 25 - Prob. 27ECh. 25 - Prob. 28ECh. 25 - Prob. 29ECh. 25 - Prob. 31ECh. 25 - Prob. 32ECh. 25 - Prob. 33ECh. 25 - Prob. 34ECh. 25 - Prob. 35ECh. 25 - Prob. 36ECh. 25 - Prob. 37ECh. 25 - Prob. 38ECh. 25 - Prob. 39ECh. 25 - Prob. 40ECh. 25 - Prob. 41ECh. 25 - Prob. 42ECh. 25 - Prob. 43ECh. 25 - Prob. 44ECh. 25 - Prob. 45ECh. 25 - Prob. 46ECh. 25 - Prob. 47ECh. 25 - Prob. 48ECh. 25 - Prob. 49ECh. 25 - Prob. 50ECh. 25 - Prob. 51E
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- (a) Find the value of for the following situation. An astronaut measures the length of his spaceship to be 100 m, while an observer measures it to be 25.0 m. (b) What is the of the spaceship relative to Earth?arrow_forwardThe truck in Figure P39.1 is moving at a speed of 10.0 m/s relative to the ground. The person on the truck throws a baseball in the backward direction at a speed of 20.0 m/s relative to the truck. What is the velocity of the baseball as measured by the observer on the ground? Figure P39.1arrow_forwardSuppose an astronaut is moving relative to Earth at a significant fraction of the speed of light. (a) Does he observe the rate of his to have slowed? (b) What change in the rate of earthbound does he see? (c) Does his ship seem to him to shorten? (d) What about the distance between two stars that lie in the direction of his motion? (e) Do he and an earthbound observer agree on his velocity relative to Earth?arrow_forward
- (a) All but the closest galaxies are receding from our own Milky Way Galaxy. If a galaxy 12.0x109ly away is receding from us at 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 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.)arrow_forwardSuppose the primed and laboratory observers want to measure the length of a rod that rests on the ground horizontally in the space between the helicopter and the tower (Fig. 39.8B). To derive the length transformation L = L (Eq. 39.5), we had to assume that the positions of the two ends were determined simultaneously. What happens to the length transformation equation if both observers measure the end below the helicopter at one time t1 and the other end at a later time t2?arrow_forwardSuppose 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?arrow_forward
- (a) What is the effective accelerating potential for electrons at the Stanford Linear Accelerator, if =1.00105 for them? (b) What is their total energy (nearly the same as kinetic in this case) in GeV?arrow_forward(a) At what relative velocity is (b) At what relative velocity isarrow_forwardAn Earth satellite used in the Global Positioning System moves in a circular orbit with period 11 h 58 min. (a) Determine the radius of its orbit. (b) Determine its speed. (c) The satellite contains an oscillator producing the principal nonmilitary GPS signal. Its frequency is 1 575.42 MHz in the reference frame of the satellite. When it is received on the Earths surface, what is the fractional change in this frequency due to time dilation, as described by special relativity? (d) The gravitational blueshift of the frequency according to general relativity is a separate effect. The magnitude of that fractional change is given by ff=Ugmc2 where Ug/m is the change in gravitational potential energy per unit mass between the two points at which the signal is observed. Calculate this fractional change in frequency. (e) What is the overall fractional change in frequency? Superposed on both of these relativistic effects is a Doppler shift that is generally much larger. It can be a redshift or a blueshift, depending on the motion of a particular satellite relative to a GPS receiver (Fig. P1.39).arrow_forward
- A spacecraft zooms past the Earth with a constant velocity. An observer on the Earth measures that an undamaged clock on the spacecraft is ticking at one-third the rate of an identical clock on the Earth. What does an observer on the spacecraft measure about the Earth-based clocks ticking rate? (a) It runs more than three times faster than his own clock. (b) It runs three times faster than his own. (c) It runs at the same rate as his own. (d) It runs at one-third the rate of his own. (e) It runs at less than one-third the rate of his own.arrow_forwardYou are on an interstellar mission from the Earth to the 8.7 light-years distant star Sirius. Your spaceship can travel with 70% the speed of light and has a cylindrical shape with a diameter of 6 m at the front surface and a length of 25 m. You have to cross the interstellar medium with anthe approximated density of 1 hydrogen atom/m3Because you are moving at an enormous speed, your mission from the previous part will be influenced by the effects of time dilation described by special relativity: Your spaceshiplaunches in June 2020 and returns back to Earth directly after arriving at Sirius.(a) How many years will have passed from your perspective?(b) At which Earth date (year and month) will you arrive back to Earth?arrow_forwardAt what relative velocity is Ƴ = 1.50 ?arrow_forward
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Length contraction: the real explanation; Author: Fermilab;https://www.youtube.com/watch?v=-Poz_95_0RA;License: Standard YouTube License, CC-BY