Question

The drag force due to air resistance on a soccer ball traveling through the air at 20 m/s is 2.3 N. What is the drag force on that same soccer ball when it is moving through the air at 35.4 m/s

Answer 1

The drag force on that same soccer ball when it is moving through the air at $35.4 m/s$ is 7.2 Newton.

Given the data in the question;

• Initial speed; $v_1 = 20m/s$

• Initial drag force; $F_1 = 2.3N$

• Final speed; $v_2 = 35.4m/s$

Final drag force; $F_2 =\ ?$

From Newton's laws, Drag force is directly proportional to velocity squared:

$F\ \alpha \ v^2 \\\\F = Kv^2$

Where k is the constant of proportionality.

Hence;

$\frac{F_1}{F_2} = \frac{V_1^2}{V_2^2}$

We make "$F_2$" the subject of the formula

$F_2 = \frac{F_1 * v_2^2}{v_1^2}$

We substitute our values into the equation;

$F_2 = \frac{2.3N * (35.4m/s)^2}{(20m/s)^2}\\\\F_2 = \frac{2.3N * 1253.16}{400} \\\\F_2 = \frac{2882.268N}{400}\\\\F_2 = 7.2N$

Therefore, the drag force on that same soccer ball when it is moving through the air at $35.4 m/s$ is 7.2 Newton.

Learn more: brainly.com/question/2867185