Chapter 9, Problem 9.1P

A slender missile is flying at Mach 1.5 at low altitude. Assume the wave generated by the nose of the missile is a Mach wave. This wave intersects the ground 559 ft behind the nose. At what altitude is the missile flying?

To determine

The altitude of flying missile.

Answer to Problem 9.1P

The altitude of flying missile is $499.98\text{ft}$ .

Explanation of Solution

Given:

The Mach number of slender missile is $M=1.5$ .

The horizontal distance is $H=559\text{ft}$ .

Formula Used:

The expression for the relation between Mach angle and Mach number is given as,

  $\sin \beta =\frac{1}{M}$

Here, $\beta$ is the Mach angle and $M$ is the Mach number.

The expression for the tan function can be given as,

  $\tan \theta =\frac{P}{B}$

Here, $\theta$ is the angle, $P$ is the perpendicular length, and $B$ is the base length.

Calculation:

The Mach angle can be calculated as,

  $\begin{array}{c}\sin \beta =\frac{1}{M}\\ \sin \beta =\frac{1}{1.5}\\ \beta ={\sin }^{-1}\left(\frac{1}{1.5}\right)\\ \beta =41.81\text{°}\end{array}$

The vertical distance can be calculated as,

  $\begin{array}{c}\tan \beta =\frac{V}{H}\\ \tan 41.81\text{°}=\frac{V}{559\text{ft}}\\ V=499.97\text{ft}\end{array}$

Conclusion:

Therefore, the altitude of missile is flying is $499.98\text{ft}$ .