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For high-speed motion through the air-such as the skydiver shown in the figure below, falling before the parachute is opened-air resistance is closer to a power of the instantaneous velocity v(t). Determine a differential equation for the velocity v(t) of a falling body of mass m if air resistance is proportional to the square of the instantaneous velocity. Assume the downward direction is positive. (Use k> 0 for the constant of proportionality. 0 for acceleration

For high-speed motion through the air-such as the skydiver shown in the figure below, falling before the parachute is opened-air resistance is closer to a power of the instantaneous velocity v(t). Determine a differential equation for the velocity v(t) of a falling body of mass m if air resistance is proportional to the square of the instantaneous velocity. Assume the downward direction is positive. (Use k> 0 for the constant of proportionality. 0 for acceleration

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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For high-speed motion through the air-such as the skydiver shown in the figure below, falling before the parachute is opened-air resistance is closer to a power of the instantaneous velocity v(t). Determine a differential equation for the velocity v(t) of a falling body of mass m if air resistance is proportional to the square of the instantaneous velocity. Assume the downward direction is positive. (Use k> 0 for the constant of proportionality, g> 0 for acceleration due to gravity, and v for v(t).) dv dt
Transcribed Image Text:For high-speed motion through the air-such as the skydiver shown in the figure below, falling before the parachute is opened-air resistance is closer to a power of the instantaneous velocity v(t). Determine a differential equation for the velocity v(t) of a falling body of mass m if air resistance is proportional to the square of the instantaneous velocity. Assume the downward direction is positive. (Use k> 0 for the constant of proportionality, g> 0 for acceleration due to gravity, and v for v(t).) dv dt
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