An imperial spaceship, moving at high speed relative to the...

Name: Problem 22, Chapter 37: University Physics with Modern Physics
Uploaded: 2019-05-06T03:44:28-08:00
Duration: 4 min 36 s
Channel: Ceren Uzun
Description: An imperial spaceship, moving at high speed relative to the planet Arrakis, fires a rocket toward the planet with a speed of 0.920c relative to the spaceship. An observer on Arrakis measures that the rocket is approaching with a speed of 0.360c. What is the speed of the spaceship relative to Arrakis? Is the spaceship moving toward or away from Arrakis?

An imperial spaceship, moving at high speed relative to the planet Arrakis, fires a rocket toward the planet with a speed of 0.920c relative to the spaceship. An observer on Arrakis measures that the rocket is approaching with a speed of 0.360c. What is the speed of the spaceship relative to Arrakis? Is the spaceship moving toward or away from Arrakis?

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Key Concepts

Sign Conventions in Relative Motion

When applying the relativistic velocity addition formula, careful attention to sign conventions is crucial. Properly defining the direction of motion (positive or negative) ensures clarity in determining whether objects are moving towards or away from one another, which is key for interpreting observed speeds in different directions.

Inertial Reference Frames

An inertial reference frame is one in which an observer is either at rest or moving at a constant velocity. Analyzing problems from different inertial frames—such as the spaceship’s frame versus the observer on the planet’s frame—is essential since measurements of speed and direction can change between these frames.

Relativistic Velocity Addition

This concept involves using the relativistic velocity addition formula to correctly combine velocities when dealing with high-speed objects. Unlike classical addition of velocities, the relativistic formula accounts for the effects of time dilation and length contraction, ensuring the resulting speed does not exceed the speed of light.

Transcript

00:01 This is chapter 37, problem number 22.

00:03 We have a planet, a rocket, and we have a spaceship moving.

00:13 We don't know the direction, actually, whether or not it's moving towards or away from the planet.

00:19 This is something that we need to find an answer to.

00:23 But let's put the s frame here, for example, for the planet, aracus.

00:29 Okay.

00:31 And then we know that the, let's put the frame of the spacecraft here.

00:37 And the space, there is a rocket launch from the spacecraft.

00:41 And the velocity, the speed of the rockets is measured.

00:49 So, so the speed of the rocket in s prime frame.

00:53 So in the spacecraft's own frame, it is, well, the prime, right, it's 0 .92 .2.

01:02 Times c.

01:04 But if we pick this to be positive x and positive x prime, then we're going to have to put a negative here, right? because the rocket is launched towards the planet.

01:15 And in the s frame, an observer measures the speed of this rocket as 0 .36c.

01:24 Again, it's going to be a negative here, right? and now we're looking for the speed of the spacecraft relative to the planet.

01:35 So let's call it a u, right? this is what we're looking for.

01:39 So let's remember the lawrence transformation.

01:44 B prime equals to b minus u over 1 minus u times v over c squared.

01:51 What we're looking for is u here...

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