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Using Newtons laws of motion we saw that while ignoring air resistance a body falling through the air, such as a skydiver, satisfies the equation m = -mg, where m is the mass of the body, g is gravity and s(t) is the height at time t. Assuming that the air resistance of such a falling body is proportional to the square of the velocity of the body, determine a differential equation for the velocity, v(t), of a falling body of mass m which takes into consideration air resistance.

Using Newtons laws of motion we saw that while ignoring air resistance a body falling through the air, such as a skydiver, satisfies the equation m = -mg, where m is the mass of the body, g is gravity and s(t) is the height at time t. Assuming that the air resistance of such a falling body is proportional to the square of the velocity of the body, determine a differential equation for the velocity, v(t), of a falling body of mass m which takes into consideration air resistance.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Using Newtons laws of motion we saw that while ignoring air resistance a body falling through the air, such as a skydiver, satisfies the equation m² = -mg, where m is the mass of the body, g is gravity and s(t) is the height at time t. Assuming that the air resistance of such a falling body is proportional to the square of the velocity of the body, determine a differential equation for the velocity, v(t), of a falling body of mass m which takes into consideration air resistance.
Transcribed Image Text:Using Newtons laws of motion we saw that while ignoring air resistance a body falling through the air, such as a skydiver, satisfies the equation m² = -mg, where m is the mass of the body, g is gravity and s(t) is the height at time t. Assuming that the air resistance of such a falling body is proportional to the square of the velocity of the body, determine a differential equation for the velocity, v(t), of a falling body of mass m which takes into consideration air resistance.
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