Solving the Sonic Boom Problem: Mach 1.60

[Mikey]

A supersonic aircraft is flying parallel to the ground. When the aircraft is directly overhead, an observer sees a rocket fired from the aircraft. Ten seconds later the observer hears the sonic boom, followed 2.80 s later by the sound of the rocket engine. What is the Mach number of the aircraft?

The answer is supposed to be 1.60. I have no idea what the rocket has to do with the aircraft... it would probably help to have an equation for the rocket and for the aircraft so that I can cancel out things like the velocity of sound in air, which I'm pretty sure I can't assume. Unfortunately, I have no idea how to get any equations knowing just the change in time. Oh, and I know that the rocket being directly overhead is important, but I can't figure what I'm supposed to get from that.

Thanks for your help!

 

[Andrew Mason]

A supersonic aircraft is flying parallel to the ground. When the aircraft is directly overhead, an observer sees a rocket fired from the aircraft. Ten seconds later the observer hears the sonic boom, followed 2.80 s later by the sound of the rocket engine. What is the Mach number of the aircraft?

The answer is supposed to be 1.60. I have no idea what the rocket has to do with the aircraft... it would probably help to have an equation for the rocket and for the aircraft so that I can cancel out things like the velocity of sound in air, which I'm pretty sure I can't assume. Unfortunately, I have no idea how to get any equations knowing just the change in time. Oh, and I know that the rocket being directly overhead is important, but I can't figure what I'm supposed to get from that.

Since the sound of the rocket takes 12.8 seconds to reach the ground from directly overhead you can work out the altitude of the airplane. The sonic boom is created by the aircraft originating at a point prior to the rocket firing. The angle of that point to the observer on the ground is a function of airplane speed in relation to the speed of sound (ie. mach number). It should be just a matter of a little trignometry after that.

AM

 

[Mikey]

Thank you!