You and Maria each own identical spaceships. As you fly past...

You and Maria each own identical spaceships. As you fly past Maria, you measure her ship to be $90 \mathrm{m}$ long and your own ship to be $100 \mathrm{m}$ long.
a. How long does Maria measure your ship to be?
b. How fast is Maria moving relative to you?

Key Concepts

Special Relativity

This is the branch of physics that deals with the laws of physics in inertial frames of reference, where the speed of light is constant in every inertial frame. It introduces concepts such as time dilation and length contraction, altering our classical understanding of space and time when objects move at speeds close to the speed of light.

Length Contraction

Length contraction is the phenomenon where the length of an object moving relative to an observer is measured to be shorter than its proper length (the length measured in the object's rest frame). It is a direct consequence of the Lorentz transformations and is only significant at speeds close to the speed of light.

Proper Length

Proper length is the length of an object measured in its own rest frame, where it is not moving relative to the observer. It serves as the invariant reference value when calculating length contraction effects in other frames where the object is in motion.

Lorentz Factor

The Lorentz factor (often denoted by ?) is a numerical factor that arises in the equations of special relativity, relating the measures of time, length, and mass between different inertial frames. It quantifies the degree of time dilation and length contraction experienced by moving objects, and is defined as ? = 1/?(1 ? v²/c²), where v is the relative velocity and c is the speed of light.

Relative Velocity

Relative velocity refers to the speed at which one object is moving with respect to another. In the context of special relativity, it is crucial because it determines the extent of relativistic effects such as time dilation and length contraction. When two observers are in uniform relative motion, each will perceive the other's clock and lengths as affected by these relativistic effects.

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