The drag force on that same soccer ball when it is moving through the air at [tex]35.4 m/s[/tex] is 7.2 Newton.
Given the data in the question;
Final drag force; [tex]F_2 =\ ?[/tex]
From Newton's laws, Drag force is directly proportional to velocity squared:
[tex]F\ \alpha \ v^2 \\\\F = Kv^2[/tex]
Where k is the constant of proportionality.
Hence;
[tex]\frac{F_1}{F_2} = \frac{V_1^2}{V_2^2}[/tex]
We make "[tex]F_2[/tex]" the subject of the formula
[tex]F_2 = \frac{F_1 * v_2^2}{v_1^2}[/tex]
We substitute our values into the equation;
[tex]F_2 = \frac{2.3N * (35.4m/s)^2}{(20m/s)^2}\\\\F_2 = \frac{2.3N * 1253.16}{400} \\\\F_2 = \frac{2882.268N}{400}\\\\F_2 = 7.2N[/tex]
Therefore, the drag force on that same soccer ball when it is moving through the air at [tex]35.4 m/s[/tex] is 7.2 Newton.
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