Question

The aerodynamic drag on a sports car depends on its shape. The car has a drag coefficient of 0.1 with the windows and the roof closed. With the windows and the roof open, the drag coefficient becomes 0.8. The car travels at 44 km/h with the windows and roof closed for the same amount of power needed to overcome the aerodynamic drag, the speed of the car with the windows and roof open (round off to two decimal places), is ______km/h. (density of air and the frontal area may be assumed to be constant).

• A. 22

Answer 1

The correct option is A 22
Case-1:
$C_{D1}=0.1$
$U_{\infty 1}$ = 44 km/h
Case-2:
$C_{D2}=0.8$
$U_{\infty 2}$ = ?
As we know, Power, P = $C_D\times \frac{1}{2}\rho U_{\infty }^3\times A$
For same power, density and frontal area,
$(power{)}_1=(power{)}_2$
$C_{D1}\frac{1}{2}{\rho }_1{A}_1{U}_{\infty 1}^3=C_{D2}\frac{1}{2}{\rho }_2{A}_2{U}_{\infty 2}^3$
$({\rho }_1={\rho }_2$)
$U_{\infty }^3\propto \frac{1}{C_D}$
${\left(\frac{U_{\infty 2}}{U_{\infty 1}}\right)}^3=\frac{C_{D1}}{C_{D2}}$
${\left(\frac{U_{\infty 2}}{44}\right)}^3=\frac{0.1}{0.8}$
$U_{\infty 2}=\frac{44}{2}=22km/h$