When you are at a height x above the surface of the earth, your weight can be found by the following formula: W(x) = mg (1 + x/R) −2 , where m is the mass of your body, g is the acceleration due to gravity, and R is the radius of the earth. For example, W(0) is your weight when you are on the surface of the earth and W(R) is your weight when you are at the height R above the surface of the earth (yes, you are far away from the earth’s atmosphere). In this question, we will approximate W(0) and W(R). (a) Find L0(x), the linear approximation of W(x) at x = 0. (b) Use L0(x) to approximate W(0) and W(R). Which approximation is more accurate? Why? (c) Find LR(x), the linear approximation of W(x) at x = R. (d) Use LR(x) to approximate W(0) and W(R). Which approximation is more accurate? Why?
When you are at a height x above the surface of the earth, your weight can be found by the following formula: W(x) = mg (1 + x/R) −2 , where m is the mass of your body, g is the acceleration due to gravity, and R is the radius of the earth. For example, W(0) is your weight when you are on the surface of the earth and W(R) is your weight when you are at the height R above the surface of the earth (yes, you are far away from the earth’s atmosphere). In this question, we will approximate W(0) and W(R). (a) Find L0(x), the linear approximation of W(x) at x = 0. (b) Use L0(x) to approximate W(0) and W(R). Which approximation is more accurate? Why? (c) Find LR(x), the linear approximation of W(x) at x = R. (d) Use LR(x) to approximate W(0) and W(R). Which approximation is more accurate? Why?
University Physics Volume 1
18th Edition
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:William Moebs, Samuel J. Ling, Jeff Sanny
Chapter1: Units And Measurement
Section: Chapter Questions
Problem 14P: The Scope and Scale of Physics Find the order of magnitude of the following physical quantities. (a)...
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When you are at a height x above the surface of the earth, your weight can be found by the following formula:
W(x) = mg (1 + x/R) −2 ,
where m is the mass of your body, g is the acceleration due to gravity, and R is the radius of the earth.
For example, W(0) is your weight when you are on the surface of the earth and W(R) is your weight when you are at the height R above the surface of the earth (yes, you are far away from the earth’s atmosphere).
In this question, we will approximate W(0) and W(R).
(a) Find L0(x), the linear approximation of W(x) at x = 0.
(b) Use L0(x) to approximate W(0) and W(R). Which approximation is more accurate? Why?
(c) Find LR(x), the linear approximation of W(x) at x = R.
(d) Use LR(x) to approximate W(0) and W(R). Which approximation is more accurate? Why?
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