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Problem 12-25: Engineering Mechanics- Dynamics (Hibbeler 14th Edition)

Engineering Mechanics Dynamics · R.C. Hibbeler · Chapter 12

Course: Engineering Mechanics Dynamics Book: R.C. Hibbeler Chapter: Chapter 12

Question

Terminal Velocity via Separable ODEs

This lesson models free-fall motion with air resistance using a separable first-order ODE of the form dv/dt = k[1 − αv²]. Students separate variables, apply partial fractions, integrate, and apply an initial condition to find an explicit velocity function involving hyperbolic tangent, then evaluate it at a specific time and determine the terminal velocity analytically.

Question:
A falling body has an acceleration defined by a equals 9.81 times the quantity one minus v-squared times ten-to-the-negative-four, in meters per second squared, where v is in meters per second and the positive direction is downward. The body is released from rest at a very high altitude. Determine: part a, the velocity when t equals 5 seconds, and part b, the body's terminal, or maximum attainable, velocity as t approaches infinity.

In this lesson, you will learn to:
• Set

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