Kevin S. Huang

2016: Problem 11

Topic: Energy
Concepts: Air resistance, Power

Solution:

To travel at velocity $v$ in the presence of air friction $f$ , we need power

P=fv

We are given $P \propto m$ and $f \propto Av^2$ so

m \propto Av^3

It remains to express $A$ in terms of $m$ . For a fixed density, $m \propto L^3$ where $L$ is the side length of the cube. Since $A=L^2$ ,

A \propto m^{2/3}

Substituting this into the previous equation,

m \propto m^{2/3}v^3

Finally we solve for $v$ ,

v^3 \propto m^{1/3}

v \propto m^{1/9}

so the answer is A.