A spaceship travels toward the Earth at a speed of 0.97 c. The occupants of the ship are standin

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A spaceship travels toward the Earth at a speed of 0.97 c....

A spaceship travels toward the Earth at a speed of $0.97 \mathrm{c}$. The occupants of the ship are standing with their torsos parallel to the direction of travel. According to Earth observers, they are about $0.50 \mathrm{~m}$ tall and $0.50 \mathrm{~m}$ wide. What are the occupants' (a) height and (b) width according to others on the spaceship?

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Key Concepts

Special Relativity

This is the physics theory which describes how measurements of space and time vary for observers moving relative to one another. It introduces fundamental concepts such as time dilation and length contraction, which are essential when analyzing objects moving at speeds close to the speed of light.

Inertial Frames

An inertial frame is a frame of reference in which an object either is at rest or moves at a constant velocity. Understanding the difference between the spaceship's rest frame and the Earth's frame is crucial, because measurements such as lengths differ between these frames due to relative motion.

Proper Length

The proper length is the length of an object measured in its own rest frame, where it is not moving. In the context of the problem, the dimensions measured by the occupants of the spaceship represent the proper lengths, which serve as a reference for calculating the effects of length contraction observed from other frames.

Length Contraction

Length contraction is a phenomenon predicted by Special Relativity whereby an object in motion is measured to be shorter along the direction of its motion relative to an observer in a different inertial frame. This effect only applies to dimensions parallel to the relative velocity, meaning that dimensions perpendicular to the motion remain unchanged.

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