Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 5: Problem 48

When a missile is shot from one spaceship toward another, it leaves the first at \(0.950 c\) and approaches the other at \(0.750 c .\) What is the relative velocity of the two ships?

Short Answer

Expert verified
The relative velocity of the two spaceships is approximately \(0.9926c\), which is very close to the speed of light. This means that the two spaceships are moving away from each other at a very high speed, almost at the speed of light.

Step by step solution

01

Understand the relativistic velocity addition formula

The relativistic velocity addition formula helps us combine velocities in situations where they are close to the speed of light (symbolized by 'c'). The formula is given as follows: \(u = \frac{v + u'}{1 + \frac{v u'}{c^2}}\) Here, \(u\) is the relative velocity of two objects, \(v\) is the velocity of one object and \(u'\) is the velocity of the other object relative to the first one. 'c' represents the speed of light.
02

Identify the given values and the unknown

From the given information, we know the velocity of the missile relative to the first spaceship and the second spaceship. We can represent them as follows: \(v = 0.950c\) \(u' = 0.750c\) We are required to find the relative velocity of the two spaceships, which is represented by 'u' in the formula.
03

Substitute the values into the formula and solve

Now, we can substitute the given values into the relativistic velocity addition formula and solve for 'u': \(u = \frac{0.950c + 0.750c}{1 + \frac{(0.950c)(0.750c)}{c^2}}\) Now, we simply need to solve the equation to find the relative velocity 'u': \(u = \frac{1.700c}{1 + \frac{(0.950c)(0.750c)}{c^2}}\) \(u = \frac{1.700c}{1 + 0.7125}\) \(u = \frac{1.700c}{1.7125}\) \(u \approx 0.9926c\)
04

Interpret the result

The relative velocity of the two spaceships is approximately \(0.9926c\), which is very close to the speed of light. This means that the two spaceships are moving away from each other at a very high speed, almost at 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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

Find the momentum of a helium nucleus having a mass of \(6.68 \times 10^{-27} \mathrm{kg}\) that is moving at \(0.200 c\)

We know that the velocity of an object with mass has an upper limit of \(c .\) Is there an upper limit on its momentum? Its energy? Explain.

(a) Show that \((p c)^{2} /\left(m c^{2}\right)^{2}=\gamma^{2}-1 .\) This means that at large velocities \(p c>>m c^{2} .\) (b) Is \(E \approx p c\) when \(\gamma=30.0, \quad\) as for the astronaut discussed in the twin paradox?

(a) Beta decay is nuclear decay in which an electron is emitted. If the electron is given \(0.750\space \mathrm{MeV}\) of kinetic energy, what is its velocity? (b) Comment on how the high velocity is consistent with the kinetic energy as it compares to the rest mass energy of the electron.

An astronaut has a heartbeat rate of 66 beats per minute as measured during his physical exam on Earth. The heartbeat rate of the astronaut is measured when he is in a spaceship traveling at \(0.5 c\) with respect to Earth by an observer (A) in the ship and by an observer (B) on Earth. (a) Describe an experimental method by which observer \(\mathrm{B}\) on Earth will be able to determine the heartbeat rate of the astronaut when the astronaut is in the spaceship. (b) What will be the heartbeat rate(s) of the astronaut reported by observers A and B?
See all solutions

Recommended explanations on Physics Textbooks

Measurements

Read Explanation

Mechanics and Materials

Read Explanation

Electricity

Read Explanation

Thermodynamics

Read Explanation

Conservation of Energy and Momentum

Read Explanation

Waves Physics

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.

Sign-up for free