Physics for beginners/10-a puzzling inconsistency

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Study this diagram carefully and you will see why Galileo and others assumed that observed velocitys add: The 40km/hr (kilometers/hour) train is shown at two different times, at 1PM to the left, and 40km away at 2PM when it is near a different clock (no timezones have been crossed!).

click image to view

The man runs on top of the train at 10km/hr. It seems reasonable to infer that the man has moved 50km in one hour (i.e., 50km/hr). This true only to the extent that the train is moving much slower than the speed of light (light moves about a million ($10^{6}$) times faster than sound.

Mathematically, this model for relative motion is the equation:

$\underbrace {{\vec {v}}_{M\mid E}} _{\text{50 km/h}}=\underbrace {{\vec {v}}_{M\mid T}} _{\text{10 km/h}}+\underbrace {{\vec {v}}_{T\mid E}} _{\text{40 km/h}},$

where:

${\vec {v}}_{M\mid E}$ is the velocity of the Man relative to Earth,

${\vec {v}}_{M\mid T}$ is the velocity of the Man relative to the Train,

${\vec {v}}_{T\mid E}$ is the velocity of the Train relative to Earth.

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Announcements

Each subpage is devoted to a chapter of Matthew Raspanti's original work. Click the image of the pdf file shown to the right to read the chapter.

• To read other works by this author visit http://www.thenatureofthings.info/index.html

CONTENTS

• Click for link to Physics for beginners as a single pdf file

00-PREFACE..(pdf) 01-INTRODUCTION..(pdf) 02-HEAVENLY MOTIONS..(pdf) 03-LAWS OF MOTION ..(pdf) 04-ENERGY ..(pdf) 05-ATOMS AND MOLECULES ..(pdf) 06-PARTICLES IN MOTION ..(pdf) 07-WAVES ..(pdf) 08-LIGHT ..(pdf) 09-ELECTROMAGNETISM ..(pdf) 10-A PUZZLING INCONSISTENCY ..(pdf)

11-THE ELUSIVE ETHER ..(pdf) 12-SPECIAL RELATIVITY ..(pdf) 13-GENERAL RELATIVITY ..(pdf) 14-INSIDE THE ATOM ..(pdf) 15-THE QUANTUM LEAP ..(pdf) 16-QUANTUM MECHANICS ..(pdf) 17-QUANTUM INTERPRETATIONS ..(pdf) 18-FUNDAMENTAL PARTICLES AND FORCES ..(pdf) 19-A COSMIC PERSPECTIVE ..(pdf) 20-POSTSCRIPT REFERENCES INDEX NOTES..(pdf)

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