Assuming that the critical velocity v c for your car is 30 mph, what is the rati

Question

Assuming that the critical velocity vc for your car is 30 mph, what is the ratio of the drag force at 30 m/s (70 mph) to the drag force at 15 m/s (35 mph), Fd(@30 m/s)/Fd(@15 m/s)?

Since v>vc the drag force is given by Equation Fd = 1/2 CDAv2 (where CD is the drag coefficient, it is a dimensionless, shape dependent constant that must be obtained from measurements. A is the cross-sectional area (r2 for a sphere), is the fluid density, and v is the speed f the object.) and the only variable that changes is the velocity.

Explanation / Answer

The drag force is given by    Fd = 0.5*CdAv2 Cd is the drag coefficient of the car A is the surface area of the car density of the air v is the speed of the car. As the only variable in the problem is speed, Fd1/Fd2 = v12/v22 Fd30/Fd15 = (30 m/s)2 / (15 m/s)2 Fd30/Fd15 = 4 Fd30/Fd15 = 4

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