The shock$-$wave cone created by the space shuttle at one instant during its reentry into the atmosphere makes an angle of $53\mathrm{.}0$ with its direction of motion. The speed of sound at this altitude is $335$ m$/$sm$/$s$.$

What is the Mach number of the shuttle at this instant?

How fast is it traveling relative to the atmosphere?

Express your answer in meters per second.

How fast is it traveling relative to the atmosphere?

Express your answer in miles per hour.

What would be its Mach number if it flew at the same speed but at low altitude where the speed of sound is $354$ m$/$sm$/$s$?$

What would be the angle of its shock$-$wave cone if it flew at the same speed but at low altitude where the speed of sound is $354$ m$/$sm$/$s$?$

Express your answer in degrees.