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2. Height of a rocket If an external force F acts upon a system whose mass varies with time, Newton's law of motion is d(mv) dm - = F + (v + u) dt dt In this equation, m is the mass of the system at time t, v is its velocity, and v + u is the velocity of the mass that is entering (or leaving) the system at the rate dm/dt. Suppose that a rocket of initial mass mo starts from rest, but is driven upward by fir- ing some of its mass directly backward at the constant rate of dm/dt = -b units per second and at constant speed relative to the rocket u =-c. The only external force acting on the rocket is F = -mg due to gravity. Under these assumptions, show that the height of the rocket above the ground at the end of t seconds (t small compared to mo/b) is то — bt, mo — bt In - žer. y = тo

2. Height of a rocket If an external force F acts upon a system whose mass varies with time, Newton's law of motion is d(mv) dm - = F + (v + u) dt dt In this equation, m is the mass of the system at time t, v is its velocity, and v + u is the velocity of the mass that is entering (or leaving) the system at the rate dm/dt. Suppose that a rocket of initial mass mo starts from rest, but is driven upward by fir- ing some of its mass directly backward at the constant rate of dm/dt = -b units per second and at constant speed relative to the rocket u =-c. The only external force acting on the rocket is F = -mg due to gravity. Under these assumptions, show that the height of the rocket above the ground at the end of t seconds (t small compared to mo/b) is то — bt, mo — bt In - žer. y = тo

Calculus: Early Transcendentals
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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2. Height of a rocket If an external force F acts upon a system whose mass varies with time, Newton's law of motion is d(mv) dm - = F + (v + u) dt dt In this equation, m is the mass of the system at time t, v is its velocity, and v + u is the velocity of the mass that is entering (or leaving) the system at the rate dm/dt. Suppose that a rocket of initial mass mo starts from rest, but is driven upward by fir- ing some of its mass directly backward at the constant rate of dm/dt = -b units per second and at constant speed relative to the rocket u =-c. The only external force acting on the rocket is F = -mg due to gravity. Under these assumptions, show that the height of the rocket above the ground at the end of t seconds (t small compared to mo/b) is то — bt, mo — bt In - žer. y = тo
Transcribed Image Text:2. Height of a rocket If an external force F acts upon a system whose mass varies with time, Newton's law of motion is d(mv) dm - = F + (v + u) dt dt In this equation, m is the mass of the system at time t, v is its velocity, and v + u is the velocity of the mass that is entering (or leaving) the system at the rate dm/dt. Suppose that a rocket of initial mass mo starts from rest, but is driven upward by fir- ing some of its mass directly backward at the constant rate of dm/dt = -b units per second and at constant speed relative to the rocket u =-c. The only external force acting on the rocket is F = -mg due to gravity. Under these assumptions, show that the height of the rocket above the ground at the end of t seconds (t small compared to mo/b) is то — bt, mo — bt In - žer. y = тo
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