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

[roflcopter]

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).

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

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.

 

[entorm]

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?

 

[roflcopter]

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!

 

[devrana01]

The nose of the super sonic missile and rocket are of blunt shape to form a bow shock wave, why?

 

[entorm]

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.

 

[devrana01]

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

 

[devrana01]

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