The following problems consider a rocket launch from Earth’s surface. The force of gravity on the rocket is given by F(d) = −mk/d^2, where m is the mass of the rocket, d is the distance of the rocket from the center of Earth, and k is a constant. 171. [T] After a certain distance D has passed, the gravitational effect of Earth becomes quite negligible, so we can approximate the force function by F(d)= { (−mk / d^2) if d < D. { 10,000 if d ≥ D. Using the value of k found in the previous exercise, find the necessary condition D such that the force function remains continuous.
The following problems consider a rocket launch from Earth’s surface. The force of gravity on the rocket is given by F(d) = −mk/d^2, where m is the mass of the rocket, d is the distance of the rocket from the center of Earth, and k is a constant. 171. [T] After a certain distance D has passed, the gravitational effect of Earth becomes quite negligible, so we can approximate the force function by F(d)= { (−mk / d^2) if d < D. { 10,000 if d ≥ D. Using the value of k found in the previous exercise, find the necessary condition D such that the force function remains continuous.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The following problems consider a rocket launch from Earth’s surface. The force of gravity on the rocket is given by F(d) = −mk/d^2, where m is the mass of the rocket, d is the distance of the rocket from the center of Earth, and k is a constant.
171.
[T] After a certain distance D has passed, the gravitational effect of Earth becomes quite negligible, so we can approximate the force function by F(d)= { (−mk / d^2) if d < D.
{ 10,000 if d ≥ D.
Using the value of k found in the previous exercise, find the necessary condition D such that the force function remains continuous.
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