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The acceleration due to gravity, g, is given by GM p2 where M is the mass of the Earth, r is the distance from the center of the Earth, and G is the uniform gravitational constant. (a) Suppose that we increase from our distance from the center of the Earth by a distance Ar = x. Use a linear approximation to find an approximation to the resulting change in g, as a fraction of the original acceleration: Ag ~ gx (Your answer will be a function of x and r.) (b) Is this change positive or negative? Ag is ? (Think about what this tells you about the acceleration due to gravity.) (c) What is the percentage change in g when moving from sea level to the top of Mount Elbert (a mountain over 14,000 feet tall in Colorado; in km, its height is 4.32 km; assume the radius of the Earth is 6400 km)? percent change =

The acceleration due to gravity, g, is given by GM p2 where M is the mass of the Earth, r is the distance from the center of the Earth, and G is the uniform gravitational constant. (a) Suppose that we increase from our distance from the center of the Earth by a distance Ar = x. Use a linear approximation to find an approximation to the resulting change in g, as a fraction of the original acceleration: Ag ~ gx (Your answer will be a function of x and r.) (b) Is this change positive or negative? Ag is ? (Think about what this tells you about the acceleration due to gravity.) (c) What is the percentage change in g when moving from sea level to the top of Mount Elbert (a mountain over 14,000 feet tall in Colorado; in km, its height is 4.32 km; assume the radius of the Earth is 6400 km)? percent change =

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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The acceleration due to gravity, g, is given by GM p2 where M is the mass of the Earth, r is the distance from the center of the Earth, and G is the uniform gravitational constant. (a) Suppose that we increase from our distance from the center of the Earth by a distance Ar = x. Use a linear approximation to find an approximation to the resulting change in g, as a fraction of the original acceleration: Ag ~ g× (Your answer will be a function of x and r.) (b) Is this change positive or negative? Ag is ? (Think about what this tells you about the acceleration due to gravity.) (c) What is the percentage change in g when moving from sea level to the top of Mount Elbert (a mountain over 14,000 feet tall in Colorado; in km, its height is 4.32 km; assume the radius of the Earth is 6400 km)? percent change =
Transcribed Image Text:The acceleration due to gravity, g, is given by GM p2 where M is the mass of the Earth, r is the distance from the center of the Earth, and G is the uniform gravitational constant. (a) Suppose that we increase from our distance from the center of the Earth by a distance Ar = x. Use a linear approximation to find an approximation to the resulting change in g, as a fraction of the original acceleration: Ag ~ g× (Your answer will be a function of x and r.) (b) Is this change positive or negative? Ag is ? (Think about what this tells you about the acceleration due to gravity.) (c) What is the percentage change in g when moving from sea level to the top of Mount Elbert (a mountain over 14,000 feet tall in Colorado; in km, its height is 4.32 km; assume the radius of the Earth is 6400 km)? percent change =
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