A plane flies at 1.25 times the speed. It's sonic boom reaches aman on the ground 1.00 min after the plan passes directly overhead.What is the altitude of the plane? Assume the speed of sound to be 330m/s.
physics - drwls, Thursday, June 10, 2010 at 10:01pm
The Mach number is 1.25. (You left out the words "of sound" in your first sentence). The Mach number can be used to get the approximate angle the shock wave makes with the horizontal. (It also depends somewhat upon the "wedge angle" of the airplane). The APPROXIMATE shock wave angle is
theta = sin^-1 (1/M) = 53.1 degrees. When the shock wave is felt, the plane has travelled 1.25*330*60s past the overhead point, or 4.95 km.
Draw yourself a figure of the situation.
The altitude H is given by
H/4.95 km = tan 53.1 = 1.332
H = 6.59 km
This problem is not as simple as they would have you believe. The shock wave angle formula is an approximation.