A spaceship traveling at 0.53c relative to the Earth sends out a rocket that travels at 0.75 as seen by viewers on Earth. If the rocket is traveling the same direction as the ship, how fast does it appear to be traveling according to viewers on the ship? give the answer to 3 decimal places, in terms of c:____________C

College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
icon
Related questions
Question
### Problem Statement

A spaceship traveling at \(0.53c\) relative to the Earth sends out a rocket that travels at \(0.75c\) as seen by viewers on Earth. If the rocket is traveling in the same direction as the ship, how fast does it appear to be traveling according to viewers on the ship? Give the answer to three decimal places, in terms of \(c\): \( \_\_\_\_\_ c \).

### Explanation

This problem involves the concept of relativistic velocity addition in the context of special relativity. The key formula for adding velocities \(u\) and \(v\) in the same direction when dealing with relativistic speeds (close to the speed of light, \(c\)) is:

\[ u' = \frac{u + v}{1 + \frac{uv}{c^2}} \]

where:
- \(u'\) is the velocity of the rocket as observed from the spaceship.
- \(u\) is the velocity of the rocket as observed from the Earth (\(0.75c\)).
- \(v\) is the velocity of the spaceship relative to the Earth (\(0.53c\)).

### Calculation

Plugging in the values:

\[ u' = \frac{0.75c + 0.53c}{1 + \frac{(0.75c)(0.53c)}{c^2}} \]

Simplifying inside the fraction:

\[ u' = \frac{0.75c + 0.53c}{1 + 0.3975} \]
\[ u' = \frac{1.28c}{1.3975} \]

Further simplifying:

\[ u' \approx 0.916c \]

### Answer

The apparent speed of the rocket as observed from the spaceship is \(0.916c\).

### Key Concepts

- **Relativistic Velocity Addition**: When velocities approach the speed of light, they do not simply add up as in classical mechanics. Instead, the formula above must be used to account for the effects of special relativity.
- **Speed of Light**: \(c\), approximately \(3 \times 10^8\) meters per second, is the maximum speed limit in the universe and plays a crucial role in relativistic equations.

### Application

This calculation is important in understanding how speeds are perceived differently by observers in different reference frames, which
Transcribed Image Text:### Problem Statement A spaceship traveling at \(0.53c\) relative to the Earth sends out a rocket that travels at \(0.75c\) as seen by viewers on Earth. If the rocket is traveling in the same direction as the ship, how fast does it appear to be traveling according to viewers on the ship? Give the answer to three decimal places, in terms of \(c\): \( \_\_\_\_\_ c \). ### Explanation This problem involves the concept of relativistic velocity addition in the context of special relativity. The key formula for adding velocities \(u\) and \(v\) in the same direction when dealing with relativistic speeds (close to the speed of light, \(c\)) is: \[ u' = \frac{u + v}{1 + \frac{uv}{c^2}} \] where: - \(u'\) is the velocity of the rocket as observed from the spaceship. - \(u\) is the velocity of the rocket as observed from the Earth (\(0.75c\)). - \(v\) is the velocity of the spaceship relative to the Earth (\(0.53c\)). ### Calculation Plugging in the values: \[ u' = \frac{0.75c + 0.53c}{1 + \frac{(0.75c)(0.53c)}{c^2}} \] Simplifying inside the fraction: \[ u' = \frac{0.75c + 0.53c}{1 + 0.3975} \] \[ u' = \frac{1.28c}{1.3975} \] Further simplifying: \[ u' \approx 0.916c \] ### Answer The apparent speed of the rocket as observed from the spaceship is \(0.916c\). ### Key Concepts - **Relativistic Velocity Addition**: When velocities approach the speed of light, they do not simply add up as in classical mechanics. Instead, the formula above must be used to account for the effects of special relativity. - **Speed of Light**: \(c\), approximately \(3 \times 10^8\) meters per second, is the maximum speed limit in the universe and plays a crucial role in relativistic equations. ### Application This calculation is important in understanding how speeds are perceived differently by observers in different reference frames, which
Expert Solution
steps

Step by step

Solved in 3 steps with 16 images

Blurred answer
Knowledge Booster
Relativistic speed and time
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
College Physics
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON