Answer
a) $8$
b) $4$
c) $P=605,000W$
$P=2,042,000W$
$P=9,454,000W$
Work Step by Step
a) $P=kA(2v)^3=8kAv^3$
b) If only the length is doubled, the area swept becomes $A_2=\pi(2r)^2=4\pi r^2=4A_1$ is doubled. Therefore, we have $P=k4Av^3=4kAv^3$
c) $P=(0.214kg/m^3)(900\pi m^2)(10m/s)^3=605,000W$
$P=(0.214kg/m^3)(900\pi m^2)(15m/s)^3=2,042,000W$
$P=(0.214kg/m^3)(900\pi m^2)(25m/s)^3=9,454,000W$
