Answer
a. $36^{\circ}$.
b. 560 m/s, Mach number 1.7.
Work Step by Step
a. See the figure provided in the textbook for this problem, or Figure 12-39.
Relate the horizontal distance that the plane has traveled when the shock wave reaches the observer, 2.0 km, to the height of the plane, 1.45 km.
$$tan\theta=\frac{1.45km}{2.0km}$$
$$\theta = tan^{-1}\frac{1.45}{2.0}=36^{\circ}$$
b. Relate the angle of the shock cone to the speed of the plane, using equation 12-5.
$$v_{obj}=\frac{v_{sound}}{sin\theta}=\frac{330\;m/s}{ sin 36^{\circ}}\approx 560m/s $$
Now find the Mach number.
$$M=\frac{v_{obj}}{v_{sound}}=\frac{1}{sin\theta}=\frac{1}{ sin 36^{\circ}}=1.7$$
