An Object of Constant Mass Is Projected Away from the Earth

question 44

Essay

An object of constant mass is projected away from the earth with initial velocity in a direction perpendicular to the earth's surface. Assuming there is no air resistance and considering the variation of the earth's gravitational field as a function of the altitude above the earth's surface, the velocity of the object satisfies the differential equation , where is the radius of the earth.
A) Solve for the velocity as a function of .
B) What is the maximum altitude of the object if its initial velocity is ?
C) Find the escape velocity, that is, the least initial velocity for which the body will not return to the earth.
(Hint: find such that .)

• A) Solve for the velocity as a function of .
• B) What is the maximum altitude of the object if its initial velocity is ?
• C) Find the escape velocity, that is, the least initial velocity for which the body will not return to the earth. (Hint: find such that .)

---

Definitions:

RNA Polymerase

An enzyme responsible for synthesizing RNA from a DNA template, playing a crucial role in gene transcription.

Alternative RNA Splicing

A post-transcriptional process in which exons or introns are selectively included in or excluded from a final mRNA transcript, thus allowing a single gene to code for multiple proteins.

Acetyl Groups

Functional groups in organic chemistry that consist of a methyl group single-bonded to a carbonyl. The formula is CH3CO-.