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Classical Mechanics Level 4

A spacecraft approaching Earth very quickly is observed at a distance of \(D.\) This has never happened before, so you check your instruments for time \(\Delta t,\) and then you check the position of the craft again.

Now you can see it at a distance of \(D- 3 c \Delta t,\) where \(c\) is the speed of light.

The craft is traveling at a constant speed of \(v\) directly toward Earth. What is \(v?\)

Assume you have made your measurements from an inertial frame very close to Earth.

\(\)
Hint: The correct solution requires no transformation.

\[\frac12 c\] \[\frac35 c\] \[\frac23 c\] \[\frac34 c\] \[\frac{999}{1000}c\] \[\frac32 c\] \[3c\]

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