**Text Transcription for Educational Website**---**Aerodynamic Drag and Car Design**3. The aerodynamic drag on a car depends on the "shape" of the car (recall that this is related to the area in the face of the direction). Notice below that the coefficient of drag is different in the two cases ([windows and roof open] vs. [windows and roof closed]).**Diagram Explanation:**- **Left Diagram:** - **Car Configuration:** Windows and roof closed - **Coefficient of Drag (CD):** 0.35 - **Visual:** A blue car with a closed roof and windows is depicted driving on a road.- **Right Diagram:** - **Car Configuration:** Windows open; roof open - **Coefficient of Drag (CD):** 0.45 - **Visual:** A blue car with an open roof and windows is depicted driving on a road.**Consideration:**Consider the car moving at 65 mph with the roof and windows closed. There is an amount of power in this situation that is required to overcome the drag force on the car. *Note that power is the product of force and velocity.***Question (a):**(a) At what velocity [mph] would the car be moving to have the same power when the roof and windows are open? Hint: this velocity will be lower than 65 mph because the car has a higher drag force in this case.---

Given data: Windows and roof closed: CD = 0.35 Windows open; roof open, CD = 0.45Power required to overcome the drag by using the following equation: P = D×U where, D is the drag force and U is the speed. The power P1 needed with windows and the roof closed is equal to the power, P2 needed with windows and roof opened. P1=P2 i.e., D1U1=D2U2 Here, U1 is the speed when the windows and the roof is closed and U2 is the speed when it open. Now, drag force, D=CD×12×ρ×U2A Where CD is the drag coefficient ρis the density of fluid and A is the frontal area. Now, (CD1×12×ρ×U12×A1)U1=(CD212×ρ×U22A2)U2 Suffixes 1 and 2 are indicate the state of window and the roof if opened or closed. Since A1=A2 CD1U13=CD2U23⇒U2=(CD1CD2)1/3×U1 Substituting the values U2=(0.350.45)1/3×65 = 59.78 mph Therefore, the speed of the car with drag coefficient 0.35 when the windows and roof opened is 59.78mph