We have been asked to investigate two flights, AA flight and U A flight. Both flights are at 33,000 feet, and the flight paths intersect directly over city of Frada Heights. A committee of concerned citizens has petitioned the City to investigate the possible danger of a collision of these two flights.
On the day we checked, we found that at 1:30 PM , AA was 32 nautical miles from Frada Heights, approaching it on a heading of 171ø at a rate of 405 knots. At the same time, United was 44 nautical miles from Frada Heights and was approaching it on a heading of 81ø at a rate of 465 knots.
The DPS has asked us to determine how fast the planes were approaching each other (i.e., how fast the distance between them was decreasing) at that time. The DPS would also like to know whether the flights would have violated the FAA's minimum separation requirement of 5 nautical miles. we would like to determine how close the planes actually get to each other.
2007-01-11 07:51:58 · 7 answers · asked by Coffee Girl 2 in Science & Mathematics ➔ Mathematics
petemeup b - people fly them. ^_^
drniles81 - maybe......who knows!
2007-01-11 08:08:43 · update #1
1ofSelby - I didn't get that answer though....how did you do it.
ironduke - exactly that's how i did it. but it seem too easy to be true.
2007-01-11 11:16:27 · update #2
My calcs show the planes approaching each other at 327 mph It will take the AA flt about 30 seconds to be over Frada Hts. It will take the UA flt 5.8 min to reach the same point. They should have a separation of approximately 35 miles by the time UA arrives at Frada Hts.
2007-01-11 08:33:46 · answer #1 · answered by 1ofSelby's 6 · 0⤊ 0⤋
The plane are flying on courses that are perpendicular to each other. Hence the distance between them at any time t is the hypotenuse of a right triangle.
Since rate times time = distance, the distance from Frada Heights at any time t is:
For AA = 32-405t and for UA = 44 -465t
Hence the distance between them at any time t is
D = sqrt[(32-405t)^2 + (44-465t)^2]
dD/dt = (760,500t -54840)/[2( 380250t^2- 54840t+2960)]^.5
Setting dDdt= 0 gives t= .079 which is the same as 32/405 which is the time for AA will be over Frada heights. So UA will be =7.265 miles away. From that point on, the distance between will increase. So separation was > than required 5 miles.
2007-01-11 09:06:27 · answer #2 · answered by ironduke8159 7 · 1⤊ 0⤋
This got me pretty stumped. All I can say for now is that the planes are coming at 90 degrees (171-81). You can use this to apply the Pythagorean theorem.
If I have time, i'll try to work out a solution later tonite.
2007-01-11 09:03:25 · answer #3 · answered by catarthur 6 · 0⤊ 0⤋
nicely i imagine the concept might want to be what did the founding fathers make the govtdepartment for, (i.e. State image). The practice would nicely be how that has labored out so a techniques and the topics that the govtdepartment has confronted over historic previous.
2016-12-29 03:49:42 · answer #4 · answered by ? 3 · 0⤊ 0⤋
I see the CIA is using Yahoo Answers to thwart terrorist plots again...
2007-01-11 08:04:47 · answer #5 · answered by drniles81 3 · 1⤊ 0⤋
i hate word problems
2007-01-11 08:20:11 · answer #6 · answered by Levi Smithe 2 · 0⤊ 0⤋
and who is flying these planes??
2007-01-11 08:01:18 · answer #7 · answered by petemeup b 3 · 0⤊ 0⤋