91影视

The formula to Mach number of the shuttle is, $\mathrm{M}=\frac{1}{\sin \mathrm{伪}}$where, M is the Mach number of the shuttle.is the angle of the shock wave.

The speed of the shuttle in m/s is $\sin \mathrm{伪}=\frac{\mathrm{v}}{{\mathrm{v}}_{\mathrm{s}}}$where, $\mathrm{伪}$is the angle of shock wave. v is the speed of sound in the air at that instant, ${\mathrm{v}}_{\mathrm{s}}$is the sonic speed of the shuttle.

The Mach number is$\mathrm{M}=\frac{\mathrm{v}}{{\mathrm{v}}_{\mathrm{s}}}$ where, M is the Mach number, ${\mathrm{v}}_{\mathrm{s}}$is the sonic speed of the shuttle. v is the speed of the sound in air.

The angle of the shock wave created by the space shuttle is 58.0 and the speed of the sound at that instant is 331 m/s. Substitute 58.0 for$\mathrm{伪}$in the above equation to find M.

$$\begin{gathered} \mathrm{M}=\frac{1}{\sin \left(58.0掳\right)} \\ =1.179 \\ =1.18 \end{gathered}$$

Therefore, The Mach number of the shuttle is 1.18

The angle of the shock wave created by the space shuttle is 58.0, the speed of the sound at that instant is 331 m/s and the Mach number of the shuttle is 1.18.Substitute 58.0 for$\mathrm{伪}$ and 331 m/s for v in the above equation to find${\mathrm{v}}_{\mathrm{s}}$

$$\begin{gathered} \sin \left({58.0}^{鈭�}\right)=\frac{\mathrm{V}}{{\mathrm{v}}_{\mathrm{s}}} \\ {\mathrm{v}}_{\mathrm{s}}=\frac{331\mathrm{m}/\mathrm{s}}{\sin \left({58.0}^{鈭�}\right)} \\ =390.31\mathrm{m}/\mathrm{s} \\ =390\mathrm{m}/\mathrm{s} \end{gathered}$$

Formula, to calculate the speed of the shuttle in mi/h is,

$$\begin{gathered} {\left({\mathrm{v}}_{\mathrm{s}}\right)}_{\mathrm{mijh}}=\left({\mathrm{v}}_{\mathrm{s}}\right)\left(\frac{6.21脳{10}^{鈭�4}\mathrm{mi}}{1\mathrm{m}}\right)\left(\frac{3600\mathrm{s}}{1\mathrm{h}}\right) \\ =(390.31\mathrm{m}/\mathrm{s})\left(\frac{6.21脳{10}^{鈭�4}\mathrm{mi}}{1\mathrm{m}}\right)\left(\frac{3600\mathrm{s}}{1\mathrm{h}}\right) \\ =872\mathrm{mi}/\mathrm{h} \end{gathered}$$

Therefore, the speed of the shuttle in m/s is 390 m/s and the speed of the shuttle in mi/h is 872 mi/h.

The Mach number is$\mathrm{M}=\frac{\mathrm{v}}{{\mathrm{v}}_{\mathrm{s}}}$Substitute 390 m/s for${\mathrm{v}}_{\mathrm{s}}$ and 344 m/s for v in the above equation to find M

role="math" localid="1668077721573" $$\begin{gathered} =\frac{390\mathrm{m}/\mathrm{s}}{344\mathrm{m}/\mathrm{s}} \\ =1.13 \end{gathered}$$

Therefore, the Mach number is 1.13

Formula to calculate the angle of the shock is$\mathrm{蝉颈苍伪}=\frac{\mathrm{v}}{{\mathrm{v}}_{\mathrm{s}}}$ Substitute 390 m/s for${\mathrm{v}}_{\mathrm{s}}$and 344 m/s for v in the above equation to find$\mathrm{伪}$

$$\begin{gathered} =\frac{344\mathrm{m}/\mathrm{s}}{390\mathrm{m}/\mathrm{s}} \\ =61.9掳 \end{gathered}$$

Therefore, the angle of the shock is$61.9掳$