Explanation Procedure used: Consider the mass of the rocket is m and the velocity of the rocket is v . Since, mass of the rocket decreases with time as it consumes fuel. Write the expression for the Newton’s second law of motion with varying mass. F = d d t ( m v ) F = m d v d t + v d m d t Write the expression for the net force acting on the rocket. F = F t − W − F a i r Here, thrust force on the rocket is F t , weight of the rocket is W and resistance force due to air is F a i r . Calculation: Considering upward thrust force on the rocket is R . Consider the force due to air resistance is directly proportional to rocket’s instantaneous velocity. Air resistance force is, F a i r = k v Here, k is a constant. Substitute k v for F a i r , R for F t and m g for W in the expression for the net force acting on the rocket

6th Edition

ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Chapter 1.3, Problem 21E

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To construct: A mathematical model for the velocity of the rocket.

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Chapter 1.3, Problem 20E

Chapter 1.3, Problem 22E

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Chapter 1 Solutions

Advanced Engineering Mathematics

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To construct: A mathematical model for the velocity of the rocket.

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