A power output from a certain experimental car design to be shaped like a cube is proportional to the mass `m` of the car. The force of air friction on the car is proportional to `Av^(2)`, where `v` is the speed of the car and `A` is the cross-sectional area. On a level surface the car has a maximum speed `v_("max")`. Assume that all versions of this design have the same density. The `v_("max")` is propotional to `m^(1//c)`. Find `C`

Explanation

At `v_("max")`
`Av_("max")^(2)=F=(km)/(v_("max"))` (where `k` is a propotionality constant)
`m^(2//3)v_("max")^(2) prop m/(v_("max"))`
`:.v_("max")prop m^(1//9)`