In the Presence of Air Resistance for an Object in Free

question 134

Essay

In the presence of air resistance for an object in free fall, the velocity is the solution of the
differential equation $\frac { d v } { d t } = g - k v$ where $g$ is the constant of acceleration due to earth's gravity and $k$ is a positive constant.(a) Find the solution for the equation that satisfies the initial value that $v ( 0 ) = 0$ .(b) As time, $t$ , increases without bound, what is the limiting velocity. (Note: the limiting velocity during free fall is called the terminal velocity.)
(c) Sketch your solution from part (a).

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Definitions:

Eating Disorder

Mental disorders characterized by abnormal eating habits that negatively affect a person's physical or mental health.

Ideal Weight

A weight range deemed optimal for an individual's height and age, considering factors like body composition, bone density, and overall health, to reduce the risk of health issues.

Fatal

Refers to something capable of causing death.

Bulimia

An eating disorder characterized by episodes of binge eating followed by methods to avoid weight gain, such as vomiting or excessive exercise.