Provide an Appropriate Response $m$ Falling from Rest Under the Action of Gravity Encounters an Falling

question 65

Multiple Choice

Provide an appropriate response.
-If a body of mass $m$ falling from rest under the action of gravity encounters an air resistance proportional to three times the square root of velocity, then the body's velocity $t$ seconds into the fall satisfies the equation: $\mathrm { m } \frac { \mathrm { dv } } { \mathrm { dt } } = \mathrm { mg } - 3 \mathrm { kv } ^ { 2 }$ where $\mathrm { k }$ is a constant that depends on the body's aerodynamic properties and the density of the air.
Determine the equilibrium, velocity curve, and the terminal velocity for a $150 \mathrm { lb }$ skydiver $( \mathrm { mg } = 150 )$ with $\mathrm { k } = 0$ .

• A) Equilibrium: \(\mathrm { v } = \sqrt { \frac { \mathrm { mg } } { 3 \mathrm { k } } }\) \(\mathrm { v } _ { \text {terminal } } = 100 \mathrm { ft } / \mathrm { sec }\)
• B) Equilibrium: \(\mathrm { v } = \sqrt { \frac { \mathrm { mg } } { 3 \mathrm { k } } }\) \(\mathrm { v } _ { \text {terminal } } = 100 \mathrm { ft } / \mathrm { sec }\)
• C) Equilibrium: \(v = \sqrt { \frac { 3 \mathrm { k } } { \mathrm { mg } } }\) \(\mathrm { v } _ { \text {terminal } } = 100 \mathrm { ft } / \mathrm { sec }\)
• D) Equilibrium: \(v = \sqrt { \frac { 3 \mathrm { k } } { \mathrm { mg } } }\) \(v _ { \text {terminal } } = 100 \mathrm { ft } / \mathrm { sec }\)

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Definitions:

Lather

The frothy foam created by agitating soap with water, commonly used for cleaning or bathing.

Rings and Watches

Personal jewelry items worn on fingers and wrists that can pose safety hazards or interfere with medical procedures if not removed.

Hot Water

Water heated to a temperature suitable for bathing, washing, or cooking.

Airborne Precautions

Safety measures implemented to prevent the transmission of diseases that are spread through the air over long distances by small droplets or particles.