Consider a supersonic missile flying at Mach 2.5 at an altitude of 10 km. Assume that the angle of the shock wave from the nose is approximated by the Mach angle (this is a very weak shock). How far behind the nose of the vehicle will the shock wave impinge upon the ground

The distance at which nose of the vehicle will the shock wave impinge upon the ground is approximately 23km

Explanation:

Let

u be Mach angle

M be Mach Number = 2.5

h be altitude = 10km

d be distance between nose of the vehicle with which the shock wave impinge upon the ground

Using;

Sin u = 1/M

u = arcSin (1/M)

u = arcSin (1/2.5) = 23.58°

Using angle at a point rule = 90°

90 - 23.58 = 66.42°

Tan A = opp/adj

Tan 66.42° = d/10

2.2911 * 10 = d

d = 22.911km ≈ 23km

1/0.14nm = 10^10/1.4 a lot