Questions: If two objects of the same size move through the air at different speeds, which encounters the greater air resistance? Both encounter the same air resistance. The one at terminal velocity encounters less air resistance. The slower object encounters more air resistance. The faster object encounters more air resistance. Submit Request Answer

If two objects of the same size move through the air at different speeds, which encounters the greater air resistance?
Both encounter the same air resistance.
The one at terminal velocity encounters less air resistance.
The slower object encounters more air resistance.
The faster object encounters more air resistance.
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Transcript text: If two objects of the same size move through the air at different speeds, which encounters the greater air resistance? Both encounter the same air resistance. The one at terminal velocity encounters less air resistance. The slower object encounters more air resistance. The faster object encounters more air resistance. Submit Request Answer

Solution

Solution Steps

Step 1: Understanding Air Resistance

Air resistance, also known as drag, is a force that opposes the motion of an object through the air. The magnitude of air resistance depends on several factors, including the speed of the object, the cross-sectional area, the density of the air, and the drag coefficient. For objects of the same size and shape moving through the same medium, the primary factor affecting air resistance is speed.

Step 2: Analyzing the Effect of Speed on Air Resistance

The relationship between speed and air resistance is such that air resistance increases with the square of the speed. Mathematically, this can be expressed as:

\[ F_d = \frac{1}{2} \cdot C_d \cdot \rho \cdot A \cdot v^2 \]

where:

\( F_d \) is the drag force (air resistance),
\( C_d \) is the drag coefficient,
\( \rho \) is the air density,
\( A \) is the cross-sectional area,
\( v \) is the velocity of the object.

From this equation, it is clear that as the velocity \( v \) increases, the drag force \( F_d \) increases quadratically.

Step 3: Determining Which Object Encounters Greater Air Resistance

Given that the two objects are of the same size and shape, the one moving at a higher speed will encounter greater air resistance due to the quadratic relationship between speed and drag force.