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A futuristic spaceship flies past Pluto with a speed of 0.964 $\mathrm{c}$relative to the surface of the planet. When the spaceship isdirectly overhead at an altitude of $1500 \mathrm{km},$ a very bright signal light on the surface of Pluto blinks on and then off. Anobserver on Pluto measures the signal light to be on for80.0$\mu$ y. What is the duration of the light pulse as measured bythe pilot of the spaceship?

$=0.301 \mathrm{ms}$

Physics 101 Mechanics

Chapter 27

Relativity

Gravitation

Cornell University

University of Washington

Simon Fraser University

McMaster University

Lectures

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Okay, So in this problem, we have ah spaceship flying with a relative speed off serial point 964 off the speed of light. We know that this spaceship is at a distance off 1000 and 500 kilometers from the surface off too. We know that the time off the link that observer ump blew to measure. It's just you're off 0.8. This should be eight 0.8 my curve seconds And the problem Just want to know what ISS did. Time measure by the person inside this issue. We know that the person inside a spaceship is under real activist IQ effects, so we know that his time is dilated. Compare with the time that you observer on the Earth measure So we can say that about t prime, which is the time of the pilot is dilated off camera Delta T. So this is just delta t prime equals delta T divided by one minus you square use ground divided by C square. All this indescribable. So if we put the values in here we have 0.8 times 10 to the minor six because this is micro seconds divided by one minus little 0.964 square all this in the square root. So if we calculate this, we're gonna get 3.1 times 10 to the minus four seconds to simplify your final answer time measure. But if Pilot is just zero point 301 merely seconds, that's your final answer. Thanks for watch.

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