A Klingon space ship moves away from the Earth at a speed of...

A Klingon space ship moves away from the Earth at a speed of $0.800 c$ (Fig. P39.25). The starship Enterprise pursues at a speed of $0.900 c$ relative to the Earth. Observers on Earth see the Enterprise overtaking the Klingon ship at a relative speed of $0.100 c$. With what speed is the Enterprise overtaking the Klingon ship as seen by the crew of the Enterprise?

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Key Concepts

Relativistic Velocity Addition

In special relativity, combining velocities from different inertial frames requires more than simply adding or subtracting them. The relativistic velocity addition formula, u' = (u - v)/(1 - uv/c²), ensures that the resultant speed never exceeds the speed of light and properly accounts for the effects of time dilation and length contraction. This concept is essential when determining how one observer in a moving frame perceives the speed of another object that is itself moving relative to a third frame.

Inertial Reference Frames

An inertial reference frame is one in which the laws of physics hold consistently and where observers are either at rest or moving at a constant velocity. In problems involving relative motion, such as objects moving at significant fractions of the speed of light, different observers in different inertial frames perceive events and measurements in unique ways. Understanding how to transform quantities such as velocity between these frames using Lorentz transformations is a key part of analyzing relativistic scenarios.

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