A spaceship whose rest length is 350 m has a speed of 0.82 c with respect to a certain referenc

step 1 A spaceship, whose rest length is 350 meters, has the speed of 0 .82c with respect to a certain

A spaceship whose rest length is 350 m has a speed of 0.82...

A spaceship whose rest length is $350 \mathrm{~m}$ has a speed of $0.82 c$ with respect to a certain reference frame. $A$ micrometeorite, also with a speed of $0.82 c$ in this frame, passes the spaceship on an antiparallel track. How long does it take this object to pass the ship as measured on the ship?

Key Concepts

Special Relativity

Special relativity is the framework that governs the behavior of objects moving at speeds close to the speed of light. It introduces the idea that measurements of space and time differ among observers in different inertial frames, and it establishes that the speed of light is the same in all such frames.

Inertial Reference Frames

An inertial reference frame is a coordinate system in which an object either is at rest or moves at a constant velocity unless acted upon by a force. Recognizing which frame is being used is crucial since physical quantities such as time intervals and lengths are measured differently depending on the observer’s frame.

Proper Length

The proper length is the length of an object measured in the frame in which the object is at rest. In problems involving relativistic speeds, this length does not suffer from length contraction and serves as a reference for comparing measurements made in other frames.

Relativistic Velocity Addition

In relativistic contexts, velocities do not simply add together as in classical mechanics. The relativistic velocity addition formula is used to determine the relative speed between two objects moving at significant fractions of the speed of light, ensuring that the resultant speed remains below the speed of light.

Time Calculation in Relativistic Contexts

When calculating the time it takes for one object to pass another in a relativistic framework, one must use the proper length and the relative speed (obtained via the relativistic velocity addition) as measured in the appropriate inertial frame. This approach properly accounts for the effects of special relativity on time measurements.

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