The shock-wave cone created by the space shuttle at one instant during its reent

Question

The shock-wave cone created by the space shuttle at one instant during its reentry into the atmosphere makes an angle of 60.0 with its direction of motion. The speed of sound at this altitude is 330 m/s .

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

B) How fast (in m/s) is it traveling relative to the atmosphere?

C) How fast (in mi/h) is it traveling relative to the atmosphere?

D) What would be its Mach number if it flew at the same speed but at low altitude where the speed of sound is 350 m/s ?

E) 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 350 m/s ?

Explanation / Answer

a) v/vs = sin alpha

v/vs = sin 60 degree

mach number = Vs/ V = 1/ sin 60 degrees = 1.155

b) Vs = V/sin 60 degrees = 330*1.155 = 381 m/s

c) Vs = 381 m/s = 852 mi/h

d) mach number = Vs/V = 381/350 =1.089

e) 1/sin alpha = 1.089

sin alpha = 1/1.089 = 0.9186

alpha = 66.7 degree

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