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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` |
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Answer» 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)` |
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