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.

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