(b) You have the ability to shut down all the engines on the spacecraft, which would allow the spacecraft to coast the rest of the way with constant velocity, as per Newton's First Law of Motion. Is there a moment, say t = c, when the captain could shut down the engines in order to allow the spacecraft to coast its way to the repair satellite? If so, calculate this exact time c. When does the spacecraft encounter the satellite? You are the captain of a spacecraft whose navigation system has malfunctioned, sending the spacecraft onto a path with position vector r(t) = 4ti + 6t2j+tk (for t≥0). Your only hope is a repair satellite located at position (x, y, z) = (28,270, 1625). Position is measured in kilometers. Time is measured in hours. (a) Show that the spacecraft will not be able to dock with the repair satellite given the present course of r(t) = 4ti + 6t²j + t'k.
(b) You have the ability to shut down all the engines on the spacecraft, which would allow the spacecraft to coast the rest of the way with constant velocity, as per Newton's First Law of Motion. Is there a moment, say t = c, when the captain could shut down the engines in order to allow the spacecraft to coast its way to the repair satellite? If so, calculate this exact time c. When does the spacecraft encounter the satellite? You are the captain of a spacecraft whose navigation system has malfunctioned, sending the spacecraft onto a path with position vector r(t) = 4ti + 6t2j+tk (for t≥0). Your only hope is a repair satellite located at position (x, y, z) = (28,270, 1625). Position is measured in kilometers. Time is measured in hours. (a) Show that the spacecraft will not be able to dock with the repair satellite given the present course of r(t) = 4ti + 6t²j + t'k.
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter8: Polar Coordinates And Parametric Equations
Section8.CT: Chapter Test
Problem 8CT
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Transcribed Image Text:(b)
You have the ability to shut down all the engines on the spacecraft, which would
allow the spacecraft to coast the rest of the way with constant velocity, as per Newton's First Law
of Motion. Is there a moment, say t = c, when the captain could shut down the engines in order to
allow the spacecraft to coast its way to the repair satellite? If so, calculate this exact time c. When
does the spacecraft encounter the satellite?
Transcribed Image Text:You are the captain of a spacecraft whose navigation system has malfunctioned, sending the
spacecraft onto a path with position vector r(t) = 4ti + 6t2j+tk (for t≥0). Your only hope is
a repair satellite located at position (x, y, z) = (28,270, 1625). Position is measured in kilometers.
Time is measured in hours.
(a)
Show that the spacecraft will not be able to dock with the repair satellite given the
present course of r(t) = 4ti + 6t²j + t'k.
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