Supersonic Jet: Mach 3 at Altitude 20,000m - Shock Wave & Boom Times

In summary, a supersonic jet traveling at Mach 3.00 at an altitude of 20,000 meters is directly over a person at a time t=0. The person will encounter the shock wave at some point in time t=t. The plane will be over the person when the "boom" is finally heard.
  • #1
roflcopter
8
0

Homework Statement



A supersonic jet traveling at Mach 3.00 at an altitude of 20,000 meters is directly over a person at a time t=0 as show in figure (see below). (a) At what time will the person encounter the the shock wave? (b) Where will the plane be when the "boom" is finally heard? (Assume the speed of sound in air is 335 m/s).

IMG_1395.jpg


This is a two part problem (a & b) and I need help with part "a" only as I've already solved part "b" on my own so far.

Homework Equations



IMG_1396.jpg


The Attempt at a Solution



Well, I solved part "b" by using sin = V/Vs with V = 1 Mach and Vs = 3 Mach to get the angle ( 19.5 degrees )

Then I used Tan = y/x solving for "x" with y=20,000 meters and Tan 19.5 degrees to get 5.66x10^4 meters.

Now for part "a" I don't have a clue how to get the time since wouldn't they just cancel out anyways by looking at the equation? I've obviously ruled out kinematics equations so...yeah.
 
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  • #2
Well, if the shock wave is generated when the plane is directly above the person, the time it will take to reach him would just be h/the speed of the shock wave, no?
 
  • #3
entorm said:
Well, if the shock wave is generated when the plane is directly above the person, the time it will take to reach him would just be h/the speed of the shock wave, no?

Ha...I totally missed that. I used d=rt and got the time.

Thanks!
 
  • #4
The nose of the super sonic missile and rocket are of blunt shape to form a bow shock wave, why?
 
  • #5
Any object moving in a fluid with a speed that exceeds the sound speed of the fluid creates a shock wave, and the shape of the shock wave depends on the shape of the object. I am not an expert on missiles or rockets, but I have the impression that their noses are actually sharp, and they are designed this way to minimize air resistance.
 
  • #6

no u r not right,they have blunt nose to create bow shock wave. it has to do some thing with local heating
 
  • #7
no u r not right,they have blunt nose to create bow shock wave. it has to do some thing with local heating
 

1. What is a supersonic jet?

A supersonic jet is an aircraft that is capable of flying faster than the speed of sound, which is approximately 343 meters per second. This means that the jet can travel at Mach 1 (equal to the speed of sound), or greater than Mach 1.

2. How fast can a supersonic jet travel?

A supersonic jet can travel at speeds of Mach 2 or greater. The exact speed depends on the specific aircraft and its capabilities, but most supersonic jets can reach speeds of Mach 3 or higher.

3. What is Mach 3?

Mach 3 is a speed that is three times the speed of sound. It is equivalent to approximately 1,233 meters per second or 2,756 miles per hour. This is the speed at which the supersonic jet in question can travel at an altitude of 20,000 meters.

4. What is a shock wave and boom time?

A shock wave is a high-pressure wave that is created by an object, such as a supersonic jet, moving faster than the speed of sound. This can cause a loud noise, known as a sonic boom, which is often heard as a loud clap or thunder-like sound. The boom time is the duration of time that the sonic boom is heard on the ground.

5. Why is shock wave and boom time important for a supersonic jet flying at Mach 3?

The shock wave and boom time are important considerations for supersonic jet flights because they can have different effects on people and structures on the ground. The loud noise from the sonic boom can be disruptive and potentially damaging, which is why supersonic jets are often limited to flying over unpopulated areas. Additionally, the shock wave can also cause disturbances in the air, which can affect other aircraft and their operations.

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