Question

which of the following descriptions best describes all of the factors that need to be considered when determining an objects terminal velocity? (1 point)
air density and the objects drag coefficient.
the objects weight and area it presents.
the objects weight and area it presents, as well as air density.
the objects weight, length, and width.

Explanation:

Step1: Recall the formula for terminal velocity

The formula for terminal velocity \(v_t=\sqrt{\frac{2mg}{
ho AC_d}}\) where \(m\) is mass (\(mg\) is weight), \(
ho\) is air density, \(A\) is the cross - sectional area of the object, and \(C_d\) is the drag coefficient.

Step2: Analyze each option

• Option 1: Only air density and drag coefficient are considered. But weight (related to \(mg\)) and area (\(A\)) are also important. So this is incorrect.
• Option 2: Only weight and area. Air density (\(

ho\)) is missing. So this is incorrect.

• Option 3: Weight (\(mg\)), area (\(A\)) and air density (\(

ho\)) are considered. Although the drag coefficient is also in the formula, if we assume a constant drag coefficient (since the question is about the main factors and in some basic considerations where drag coefficient is taken as a property of the object's shape and we are comparing objects in the same medium), this option covers the major variable factors.

• Option 4: Length and width (which would be used to calculate area, but just length and width without considering air density is wrong). Also, weight is considered but air density is missing. So this is incorrect.

Answer:

The object’s weight and area it presents, as well as air density.