/*! 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 31 As observed from Earth, rocket A... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 26: Problem 31

As observed from Earth, rocket Alpha moves with speed \(0.90 c\) and rocket Bravo travels with a speed of \(0.60 c\) They are moving along the same line toward a head-on collision. What is the speed of rocket Alpha as measured from rocket Bravo? (tutorial: adding velocities)

Short Answer

Expert verified
Answer: The relative velocity of rocket Alpha as seen from rocket Bravo is approximately 0.65217c or 65.217% of the speed of light.

Step by step solution

01

Identify the given information

We are given the velocities of rocket Alpha and rocket Bravo as observed from Earth or in the Earth's frame. - Velocity of rocket Alpha, \(v_A = 0.90c\) - Velocity of rocket Bravo, \(v_B = 0.60c\) We want to find the velocity of rocket Alpha as measured from rocket Bravo.
02

Apply the Einstein velocity addition formula

The Einstein velocity addition formula is used to add velocities in Special Relativity. The formula is given by: \(u = \frac{v_A + v_B}{1 + \frac{v_A v_B}{c^2}}\) where \(u\) is the relative velocity of rocket Alpha as measured from rocket Bravo, \(v_A\) is the velocity of rocket Alpha, \(v_B\) is the velocity of rocket Bravo, and \(c\) is the speed of light.
03

Insert the given values into the formula and solve

Plugging the given values into the formula, we get: \(u = \frac{0.90c - 0.60c}{1 + \frac{(0.90c)(-0.60c)}{c^2}}\) Notice that for rocket Bravo, its speed is in the opposite direction, so its value becomes negative. Simplify the expression and solve for \(u\): \(u = \frac{0.30c}{1 - 0.54}\) \(u = \frac{0.30c}{0.46}\) \(u = 0.65217c\)
04

Report the final answer

The speed of rocket Alpha as measured from rocket Bravo is approximately \(0.65217c\) or \(65.217\%\) of the speed of light.

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 cosmic ray particle travels directly over a football field, from one goal line to the other, at a speed of \(0.50 c .\) (a) If the length of the field between goal lines in the Earth frame is \(91.5 \mathrm{m}(100 \mathrm{yd}),\) what length is measured in the rest frame of the particle? (b) How long does it take the particle to go from one goal line to the other according to Earth observers? (c) How long does it take in the rest frame of the particle?

A white dwarf is a star that has exhausted its nuclear fuel and lost its outer mass so that it consists only of its dense, hot inner core. It will cool unless it gains mass from some nearby star. It can form a binary system with such a star and gradually gain mass up to the limit of 1.4 times the mass of the Sun. If the white dwarf were to start to exceed the limit, it would explode into a supernova. How much energy is released by the explosion of a white dwarf at its limiting mass if \(80.0 \%\) of its mass is converted to energy?
For a nonrelativistic particle of mass \(m,\) show that \(K=p^{2} /(2 m) .\) [Hint: Start with the nonrelativistic expressions for kinetic energy \(K\) and momentum \(p\).]
The light-second is a unit of distance; 1 light-second is the distance that light travels in 1 second. (a) Find the conversion between light-seconds and meters: 1 lightsecond \(=? \mathrm{m} .\) (b) What is the speed of light in units of light-seconds per second?
Radon decays as follows: $^{222} \mathrm{Rn} \rightarrow^{218} \mathrm{Po}+\alpha .$ The mass of the radon-222 nucleus is 221.97039 u, the mass of the polonium- 218 nucleus is \(217.96289 \mathrm{u},\) and the mass of the alpha particle is 4.00151 u. How much energy is released in the decay? \(\left(1 \mathrm{u}=931.494 \mathrm{MeV} / \mathrm{c}^{2} .\right)\)
See all solutions

Recommended explanations on Physics Textbooks

Space Physics

Read Explanation

Linear Momentum

Read Explanation

Physical Quantities And Units

Read Explanation

Torque and Rotational Motion

Read Explanation

Fields in Physics

Read Explanation

Thermodynamics

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.