The following problems consider a rocket launch from Earth’s surface. The force of gravity on the rocket is given by F(d)=−mk/d2, 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. 172. As the rocket travels away from Earth’s surface, there is a distance D where the rocket sheds some of its mass, since it no longer needs the excess fuel storage. We can write this function as F(d)=⎨(−m↓1 k / d^2) if d < D (−m↓2 k / d^2) if d ≥ D Is there a D value such that this function is continuous, assuming m1≠m2?
Recall the discussion on spacecraft from the chapter opener. The following problems consider a rocket launch from Earth’s surface. The force of gravity on the rocket is given by F(d)=−mk/d2, 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.
172.
As the rocket travels away from Earth’s surface, there is a distance D where the rocket sheds some of its mass, since it no longer needs the excess fuel storage. We can write this function as F(d)=⎨(−m↓1 k / d^2) if d < D
(−m↓2 k / d^2) if d ≥ D
Is there a D value such that this function is continuous, assuming m1≠m2?
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