The Pitot tube on a supersonic aircraft (see the Video) cruising at an altitude of 35000 ft senses a stagnation pressure of 9.5 psia. If the atmosphere is considered standard, determine (a) the Mach number of the aircraft, (b) the airspeed.

A) Mach number = 1.25

B) Airspeed = 1241.79 m/s

Explanation:

A) From the 1st image attached of the physical properties of air at standard atmospheric pressure; at 35000 ft, by interpolation, we will get a pressure(p) of 3.7 lb/in². From the question, stagnation pressure(Ps) = 9.5 psia or 9.5 lb/in².

Pressure ratio is given as; Ps/P

Thus, pressure ratio = 9.5/3.7 = 2.566

This ratio is tied to mach number and the mach number and from the second image attached, it's calculated to be approximately 1.25

B) From the first image, from interpolation and at altitude of 35000 ft, Temperature is approximately - 49.2°F.

Now,we need to convert it to degree rankine. Thus temperature (T) = - 49.2 + 460 = 410.8 °R

Gas constant (R) for air when converted to ft.lb/slug °R gives; R=1716 ft.lb/slug °R

Also,for the specific heat ratio, we will use the standard value which is k = 1.4

Now, the speed of sound is given by the equation;

c = √(RkT) = √(1716 x 1.4 x 410.8) = √(986905.92) = 993.43 ft/s

Now for us to calculate the aircraft speed, we will do it from the Mach number equation which is;

Ma = V/c

Where Ma is mach number and V is speed of aircraft and c is speed of sound. In this case, speed of aircraft is equal to the speed of the air relative to the aircraft's system.

Thus, V =cMa = 993.43 x 1.25 = 1241.79 m/s

when jerome paddle in flowing river towards east the net speed of jerome will increase

so the net speed of jerome will be given as

now the speed of paul will be same as it is given as he is running on the ground

so

so here we can say since the speed of jerome is more so he will win the race

now as we know the distance so the time difference is given as

so jerome will reach first and the time difference will be 203.55 s or 3.4 min

it's a b and