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

To solve the problem, we need to establish the relationship between the maximum speed \( v_{\text{max}} \) of the car and its mass \( m \). We will follow the steps outlined in the video transcript to derive the value of \( C \).

### Step-by-Step Solution:

1. **Understanding Power Output**:
The power output \( P \) of the car is proportional to its mass \( m \). Thus, we can write:
\[
P \propto m
...