Consider a hypersonic vehicle with a spherical nose flying at Mach 20 at a standard altitude of 150,000 ft, where the ambient temperature and pressure are 500^◦R and 3.06 lb./ft², respectively. At the point on the surface of the nose located 20^◦ away from the stagnation point, estimate the: 

(a) Pressure, 

(b) Temperature, 

(c) Mach number, 

(d) Velocity of the flow.