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 (the density of air and frontal area may be assumed to be constant).
Answer :
22
The power needed to overcome the aerodynamic drag is given by Fd•V
Where, Fd= is the drag force given by
Fd= Cd ρAV²/2
For the power to remain same in both the cases of windows closed and open, then
(Fd • V)windows closed =(Fd • V)windows closed
or,
(Cd ρAV3/2)windows closed = (Cd ρAV3/2)windows closed
Or, 0.1•44³ = 0.8 • V3
V = 22km/h
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