how fast must a car with 40 square feet of surface area travel in order to experience a wind resistance of 270 Newton?

Question

Wind resistance varies jointly as an object’s surface area and velocity. If an object traveling at 40 miles per hour with the surface area of 25 square feet experiences a wind resistance of 225 Newton, how fast must a car with 40 square feet of surface area travel in order to experience a wind resistance of 270 Newton?

Answer 1

In the first case, speed times area is

 

(40 mph)(25 ft²) = 1000 mph ft²,

 

which corresponds to to 225 N of resistance.  In the second case, v(40 ft²) corresponds to 270 N.  The ratio of resistance to product of speed and area should be the same for both.  Then

 

(225 N)/(1000 mph ft²) = (270 N) / [v(40 ft²)] ⇒

 

0.225 = 6.75/v

 

v = 30 mph