Answer
(a) The person should leave at least 95 km away from the airport runway.
(b) The friend experiences an intensity of $2.5\times 10^{-7}~W/m^2$
(c) $P = 1.13\times 10^5~W$
Work Step by Step
(a) We can find the radius $r_2$ where we can preserve our peace of mind.
$\frac{r_2^2}{r_1^2} = \frac{I_1}{I_2}$
$r_2 = \sqrt{\frac{I_1}{I_2}}~r_1$
$r_2 = \sqrt{\frac{10.0~W/m^2}{1.0\times 10^{-6}~W/m^2}}~(30.0~m)$
$r_2 = 95,000~m = 95~km$
The person should live at least 95 km away from the airport runway.
(b) We can find the intensity $I_3$ that the friend experiences. Note that $r_3 = 2~r_2 = 190,000~m$
$\frac{r_3^2}{r_1^2} = \frac{I_1}{I_3}$
$I_3 = \frac{I_1~r_1^2}{r_3^2}$
$I_3 = \frac{(10.0~W/m^2)(30.0~m)^2}{(190,000~m)^2}$
$I_3 = 2.5\times 10^{-7}~W/m^2$
The friend experiences an intensity of $2.5\times 10^{-7}~W/m^2$
(c) We can find the power that the jet produces.
$P = I_1~A_1$
$P = I~(4\pi~r_1^2)$
$P = (10.0~W/m^2)~(4\pi)(30.0~m)^2$
$P = 1.13\times 10^5~W$
