A particle of mass (m) travels between two points (x=0) and (x=x_{1}) on Earth's surface, leaving at

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A particle of mass \(m\) travels between two points \(x=0\) and \(x=x_{1}\) on Earth's surface, leaving at time \(t=0\) and arriving at \(t=t_{1}\). The gravitational field \(g\) is uniform.

(a) Suppose \(m\) moves along the ground (keeping altitude \(z=0\) ) at steady speed. Find the total action \(S\) to go by this path.

(b) Suppose instead that \(m\) moves along the least-action parabolic path. Show that the action in this case is

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and verify that it is less than the action for the straight-line path of part (a).

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Modern Classical Mechanics

ISBN: 9781108834971

1st Edition

Authors: T. M. Helliwell, V. V. Sahakian

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Question Posted: Mar 16, 2024 11:28 AM

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A particle of mass (m) travels between two points (x=0) and (x=x_{1}) on Earth's surface, leaving at

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mx mg S= 211 24

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Obviously thi...View the full answer

Modern Classical Mechanics

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