/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 3 A spaceship traveling at speed \... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 26: Problem 3

A spaceship traveling at speed \(0.13 c\) away from Earth sends a radio transmission to Earth. (a) According to Galilean relativity, at what speed would the transmission travel relative to Earth? (b) Using Einstein's postulates, at what speed does the transmission travel relative to Earth?

Short Answer

Expert verified
Question: A spaceship is traveling at a speed of 0.13c away from Earth and sending a radio transmission back to Earth. Calculate the speed of the radio transmission relative to Earth using (a) Galilean relativity, and (b) Einstein's postulates. Answer: (a) Using Galilean relativity, the radio transmission travels at a speed of 0.87c relative to Earth. (b) Using Einstein's postulates, the radio transmission travels at a speed of c relative to Earth.

Step by step solution

01

Analyze Galilean Relativity

According to Galilean relativity, the relative speed between two objects is simply the difference between their two speeds. For this problem, the speed of the spaceship is given as 0.13c, and the speed of light is represented by c.
02

Calculate speed of radio transmission using Galilean relativity

Using the Galilean rule, we can find the speed of the radio transmission relative to Earth by subtracting the speed of the spaceship from the speed of light: Relative speed = c - 0.13c Relative speed = (1 - 0.13)c Relative speed = 0.87c In Galilean relativity, the radio transmission travels at a speed of 0.87c relative to Earth.
03

Analyze Einstein's Postulates

According to Einstein's postulates, one of the main principles of special relativity is that the speed of light in a vacuum is constant and does not depend on the motion of the source or the observer. Therefore, the speed of the radio transmission relative to Earth should be equal to the speed of light in a vacuum, c.
04

Calculate speed of radio transmission using Einstein's postulates

Using Einstein's postulates of special relativity, the radio transmission travels at a constant speed of light in a vacuum, c, which is the same relative to Earth. So, according to Einstein's postulates, the radio transmission travels at a speed of c relative to Earth. To summarize the answers: (a) Using Galilean relativity, the radio transmission travels at a speed of 0.87c relative to Earth. (b) Using Einstein's postulates, the radio transmission travels at a speed of c relative to Earth.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A spaceship resting on Earth has a length of \(35.2 \mathrm{m} .\) As it departs on a trip to another planet, it has a length of \(30.5 \mathrm{m}\) as measured by the Earthbound observers. The Earthbound observers also notice that one of the astronauts on the spaceship exercises for 22.2 min. How long would the astronaut herself say that she exercises?
Two spaceships are moving directly toward one another with a relative velocity of \(0.90 c .\) If an astronaut measures the length of his own spaceship to be \(30.0 \mathrm{m},\) how long is the spaceship as measured by an astronaut in the other ship?
Derivation of the Doppler formula for light. A source and receiver of EM waves move relative to one another at velocity \(v .\) Let \(v\) be positive if the receiver and source are moving apart from one another. The source emits an EM wave at frequency \(f_{\mathrm{s}}\) (in the source frame). The time between wavefronts as measured by the source is \(T_{\mathrm{s}}=1 / f_{\mathrm{s}}\) (a) In the receiver's frame, how much time elapses between the emission of wavefronts by the source? Call this \(T_{\mathrm{T}}^{\prime} .\) (b) \(T_{\mathrm{T}}^{\prime}\) is not the time that the receiver measures between the arrival of successive wavefronts because the wavefronts travel different distances. Say that, according to the receiver, one wavefront is emitted at \(t=0\) and the next at \(t=T_{\mathrm{o}}^{\prime} .\) When the first wavefront is emitted, the distance between source and receiver is \(d_{\mathrm{r}}\) When the second wavefront is emitted, the distance between source and receiver is \(d_{\mathrm{r}}+v T_{\mathrm{r}}^{\prime} .\) Each wavefront travels at speed \(c .\) Calculate the time \(T_{\mathrm{r}}\) between the arrival of these two wavefronts as measured by the receiver. (c) The frequency detected by the receiver is \(f_{\mathrm{r}}=1 / T_{\mathrm{r}} .\) Show that \(f_{\mathrm{r}}\) is given by $$f_{\mathrm{r}}=f_{\mathrm{s}} \sqrt{\frac{1-v / \mathrm{c}}{1+v / \mathrm{c}}}$$
The solar energy arriving at the outer edge of Earth's atmosphere from the Sun has intensity \(1.4 \mathrm{kW} / \mathrm{m}^{2}\) (a) How much mass does the Sun lose per day? (b) What percent of the Sun's mass is this?
A starship takes 3.0 days to travel between two distant space stations according to its own clocks. Instruments on one of the space stations indicate that the trip took 4.0 days. How fast did the starship travel, relative to that space station?
See all solutions

Recommended explanations on Physics Textbooks

Magnetism and Electromagnetic Induction

Read Explanation

Quantum Physics

Read Explanation

Nuclear Physics

Read Explanation

Energy Physics

Read Explanation

Conservation of Energy and Momentum

Read Explanation

Electrostatics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.