A rocket lifts off the pad at Cape Canaveral. According to Newton's Law of Gravitation, the force of gravity on the rocket s given by GMm F(x) = - x2 where M is the mass of the earth, m is the mass of the rocket, G is a universal constant, and x is the distance (in miles) between the rocket and the center of the earth. Take the radius of the earth to be 4000 miles, so that x > 4000 miles. Find the work, W,, done against gravity when the rocket rises 1600 miles. W = | GMm (mile-pounds) Next, find the limit of the work, W2, as the rocket rises infinitely far from the earth. W2 = GMm (mile-pounds)
A rocket lifts off the pad at Cape Canaveral. According to Newton's Law of Gravitation, the force of gravity on the rocket s given by GMm F(x) = - x2 where M is the mass of the earth, m is the mass of the rocket, G is a universal constant, and x is the distance (in miles) between the rocket and the center of the earth. Take the radius of the earth to be 4000 miles, so that x > 4000 miles. Find the work, W,, done against gravity when the rocket rises 1600 miles. W = | GMm (mile-pounds) Next, find the limit of the work, W2, as the rocket rises infinitely far from the earth. W2 = GMm (mile-pounds)
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:A rocket lifts off the pad at Cape Canaveral. According to Newton's Law of Gravitation, the force of gravity on the rocket is given by
GMm
F(x) = -
x2
where M is the mass of the earth, m is the mass of the rocket, G is a universal constant, and x is the distance (in miles) between the rocket and the center of the earth. Take the radius of the earth to
be 4000 miles, so that x > 4000 miles.
Find the work, W1, done against gravity when the rocket rises 1600 miles.
W =
GMm (mile-pounds)
Next, find the limit of the work, W2, as the rocket rises infinitely far from the earth.
W2 =
GMm (mile-pounds)
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