Question

A student drops a feather off the top a building. The feather averages 1.5m/s while
fluttering to the ground.
Determine all unknowns.

Answer 1

The acceleration with which an object falls through a fluid decreases as the speed of the object increases under gravity, to the point where the speed becomes constant, which is known as the terminal speed of the object

The unknown parameters are the mass of the feather, the density of the air, the feather's projected area and the coefficient of drag

The reason the above selected parameters are the correct unknowns is as follows;

The known parameter;

The speed of the feather the student drops off the building's top = 1.5 m/s

The required parameter;

The unknown parameters

Method;

Determine the terminal velocity parameters of the feather

The terminal velocity, $\mathbf{V_t}$, of an item is the maximum steady speed the item reaches as it falls through a fluid. The terminal velocity of the feather is given by the following equation

$Terminal \ velocity, V_t = \mathbf{\sqrt{\dfrac{2 \cdot m \cdot g}{\rho \cdot A \cdot C_d} }}$

Where;

$\mathbf{V_t}$ = Terminal velocity = The constant speed of the feather

m = Mass of the feather

g = Gravitational acceleration

ρ = Air density

A = The feather's projected area

$C_d$ = Drag coefficient

The average speed of the feather = 1.5 m/s = The feathers typical or most common speed = The terminal velocity of the feather, $\mathbf{V_t}$;

Plugging in $\mathbf{V_t}$ = 1.5 m/s gives;

$V_t = 1.5 \ m/s = \mathbf{\sqrt{\dfrac{2 \cdot m \cdot g}{\rho \cdot A \cdot C_d} }}$

Therefore, the unknown parameters with regard to the feather falling are the parameters that are to be specified, including;

• The mass of the feather

• The density of air at the location

• The feather's projected area

• The drag coefficient

Learn more about terminal velocity here:

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