Question

Jet planes can exceed the speed of sound . The mach number describes the speed of such planes. Mach 2 is twice the speed of sound. The speed of sound in air is approximately 344m/sec. complete parts a-c below:a. if the speed of a plane is described as Mach 2.5 what is it's speed in kilometers per hour? b. if the speed of a plane is described as Mach 3.8, what is it's speed in meters per second?c. Describe the speed of 3150 km/hr as a Mach number.

Answer 1

Since Mach 2 is twice the speed of sound and the speed of sound is 344 m/sec, then Mach 2 is

$2\times344=688\text{ m/sec}$

a.

If the speed of a plane is Mach 2.5, then

$\frac{2}{2.5}=\frac{688}{x}$

By using cross multiplication

$\begin{gathered} 2\times x=2.5\times688 \\ 2x=1720 \end{gathered}$

Divide both sides by 2

$x=860\text{ m/sec}$

Now we need to change it to km per h

Since 1 km = 1000 m, 1 h = 60 x 60 = 3600 sec, then

$\frac{\frac{860}{1000}}{\frac{1}{3600}}=3096\text{ km/h}$

b.

Since the speed of the plane is Mach 3.8, then

$\frac{2}{3.8}=\frac{688}{y}$

By using cross multiplication

$\begin{gathered} 2\times y=3.8\times688 \\ 2y=2614.4 \end{gathered}$

Divide both sides by 2

$\begin{gathered} \frac{2y}{2}=\frac{2614.4}{2} \\ y=1307.2\text{ m/sec} \end{gathered}$

The speed is 1307.2 m/sec

c.

Since the speed is 3150, then

Change it to m/sec

$\frac{3150\times1000}{1\times60\times60}=875\text{ m/sec}$

Now let us find the Mach number

$\frac{2}{z}=\frac{688}{875}$

By using cross multiplication

$\begin{gathered} 688\times z=2\times875 \\ 688z=1750 \end{gathered}$

Divide both sides by 688

$\begin{gathered} \frac{688z}{688}=\frac{1750}{688} \\ z=2.5436 \end{gathered}$

The Mach number is about 2.544