28. (a) Suppose that a body is dropped (vo = 0) from a dis- tance ro > R from the earth's center, so its acceleration is dv/dt = -GM/r?. Ignoring air resistance, show that it reaches the height r < ro at time ro Vrro - r2 + ro cos 2GM ro (Suggestion: Substitute r = ro cos² 0 to evaluate S Vr/(ro – r)dr.) (b) If a body is dropped from a height of 1000 km above the earth's surface and air resistance is neglected, how long does it take to fall and with what speed will it strike the earth's surface?

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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28. (a) Suppose that a body is dropped (vo = 0) from a dis-
tance ro > R from the earth's center, so its acceleration
is dv/dt = -GM/r?. Ignoring air resistance, show that it
reaches the height r < ro at time
ro
Vrro - r2 + ro cos
2GM
ro
(Suggestion: Substitute r = ro cos² 0 to evaluate
S Vr/(ro – r)dr.) (b) If a body is dropped from a height
of 1000 km above the earth's surface and air resistance
is neglected, how long does it take to fall and with what
speed will it strike the earth's surface?
Transcribed Image Text:28. (a) Suppose that a body is dropped (vo = 0) from a dis- tance ro > R from the earth's center, so its acceleration is dv/dt = -GM/r?. Ignoring air resistance, show that it reaches the height r < ro at time ro Vrro - r2 + ro cos 2GM ro (Suggestion: Substitute r = ro cos² 0 to evaluate S Vr/(ro – r)dr.) (b) If a body is dropped from a height of 1000 km above the earth's surface and air resistance is neglected, how long does it take to fall and with what speed will it strike the earth's surface?
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