Meriam, Kraige & Bolton — Kinetics of Particles: Problem 3_281

3/281 The retarding forces which act on the racecar are the drag force \(F_D\) and a nonaerodynamic force \(F_R\). The drag force is \(F_D = C_D(\frac{1}{2} \rho v^2)S\), where \(C_D\) is the drag coefficient, \(\rho\) is the air density, \(v\) is the car speed, and \(S = 30 \text{ ft}^2\) is the projected frontal area of the car. The nonaerodynamic force \(F_R\) is constant at \(200 \text{ lb}\). With its sheet metal in good condition, the racecar has a drag coefficient \(C_D = 0.3\) and it has a corresponding top speed \(v = 200 \text{ mi/hr}\). After a minor collision, the damaged front-end sheet metal causes the drag coefficient to be \(C_D' = 0.4\). What is the corresponding top speed \(v'\) of the racecar?