Problem $3$:

The command module has performed a deorbit burn and is reentering Earth's atmosphere at a velocity of $\backslash (28,512\mathrm{.}844\backslash$mathrm$\{$ft$\}/\backslash$mathrm$\{$s$\}\backslash )$ and at an entry angle relative to the local horizontal of $18\mathrm{.}171$ degrees on a ballistic trajectory.

The vehicle is returning with a weight of $14,056\mathrm{.}981$ lbf$.$

The parachutes will deploy when the velocity has reduced to $\backslash (100\backslash$mathrm$\{$ft$\}/\backslash$mathrm$\{$s$\}\backslash ).$

Determine the geopotential altitude where the parachutes should deploy for these entry conditions.

NOTE: The drag coefficient of the vehicle is estimated to be C$\_$D $=1\mathrm{.}324,$ and the capsule has a planform area of $\backslash (\backslash$mathrm$\{$S$\}=141\backslash$mathrm$\{$ft$\}^\{\backslash$wedge$\}2\backslash ).$

NOTE: The gravitational constant at sea level should taken as go $\backslash (=32\mathrm{.}2\backslash$mathrm$\{$ft$\}/\backslash$mathrm$\{$s$\}^\{\backslash$wedge$\}2\backslash )$ and the specific gas constant for air is $\backslash (\backslash$mathrm$\{$R$\}=1716\mathrm{.}46\backslash$mathrm$\{$ft$\}\backslash$mathrm$\{$lbf$\}/\backslash )$ slug Rankine.

NOTE: You can treat the Earth's atmosphere as isothermal with a temperature of $\backslash (\backslash$mathrm$\{$T$\}=\backslash )518\mathrm{.}69$ Rankine.

Express your answer in ft up to $3$ decimal places.

Problem $3\mathrm{.}1$:

Please enter the ballistic parameter in $($slug$/$ft$2)$ up to $5$ decimal places:

Problem $3\mathrm{.}2$:

Please enter the density at the altitude at which the parachutes should deploy in $($slug$/\backslash (\backslash$mathrm$\{$ft$\}\_\{3\}\backslash ))$ up to $5$ significant digits: