Chapter 10.4, Problem 82AYU

Sonic Boom Aircraft such as fighter jets routinely go supersonic ( faster than the speed of sound ). An aircraft moving faster than the speed of sound produces a cone-shaped shock wave that “booms" as it trails the vehicle. The wave intersects the ground in the shape of one half of a hyperbola and the area over which the "boom" is audible is called the “boom carpet”. If an aircraft creates a shock wave that intersect the ground in the shape of the hyperbola $\frac{x^2}{484}-\frac{y^2}{100}=1$(units in miles), how wide is the 'boom carpet" $32$ miles behind the aircraft?