| Now a bit of info about flying saucers (and airplanes too). | ||||||||
| The speed that an airplane travels over the ground | ||||||||
| is a combination of two things. | ||||||||
| One is the speed that it moves through the air | ||||||||
| (called airspeed). | ||||||||
| The other is the speed that the air is moving | ||||||||
| (called wind). | ||||||||
| Human pilots try to fly routes where the wind is blowing | ||||||||
| in the same direction that they are flying. | ||||||||
| That lets them move faster over the ground. | ||||||||
| They get to the destination faster and use less fuel. | ||||||||
| (Alien's probably do the same thing, | ||||||||
| but I've never had the chance to ask.) | ||||||||
| Example: | ||||||||
| The wind is blowing from the north to the south | ||||||||
| at 10 miles per hour. | ||||||||
| Two airplanes leave the same airport at the same time | ||||||||
| AND TRAVEL AT THE SAME AIRSPEED. | ||||||||
| One travels north (into the wind) | ||||||||
| The other travels south (with the wind) | ||||||||
| At some time later, the one that was traveling north | ||||||||
| is 200 miles from the airport. | ||||||||
| The one traveling south is 235 miles from the airport. | ||||||||
|
What is the airspeed of the two planes? |
||||||||
| The problems are starting to get more involved. | ||||||||
| We are going to use: | ||||||||
| D for distance | ||||||||
| R for rate (the speed the plane flies OVER THE GROUND) | ||||||||
| T for time. | ||||||||
| We also need to tell the two planes apart. | ||||||||
| To do this, we call the plane going north plane 1. | ||||||||
| Then we can call the distance it went D1 | ||||||||
| and the speed it went over the ground R1 | ||||||||
| and the time it traveled T1. | ||||||||
| We can also call the plane that went south, plane 2. | ||||||||
| Plane 2 can use D2 , R2 , and T2 for it's distance, rate and time. | ||||||||
| So what of these things do we know? | ||||||||
|
||||||||
| Here's what we do. | ||||||||
| We have too many things that are unknown. | ||||||||
| We need to get rid of a few of them. | ||||||||
| We don't know either of the times, | ||||||||
| but we know that they are the same. | ||||||||
| That means we can write them both as T. | ||||||||
| The ground speeds of the two planes | ||||||||
| are different because of the wind. | ||||||||
| But the airspeeds are the same. | ||||||||
| If we call the airspeed r, then | ||||||||
| R1 = r -10 and R2 = r + 10. | ||||||||
| The DRT equations for the two planes are: | ||||||||
|
D1 = R1 x T and D2 = R2 x T |
||||||||
| Substituting what we know, we have ... | ||||||||
|
200 = (r - 10) x T and 235 = (r + 10) x T |
||||||||
| Now we have two equations with 2 unknowns. | ||||||||
| There are a lot of ways that we can solve these. | ||||||||
| In the way we are going to use, | ||||||||
| the first step is to turn them each around to be: | ||||||||
|
T = "Stuff" |
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|
|
||||||||
| Here's the tricky part. | ||||||||
| Since "T" is the same in both equations, | ||||||||
| we can say ... | ||||||||
|
|
||||||||
| and actually, we don't even need the "T" ... | ||||||||
|
|
||||||||
| Now we solve for "r" (which is the airspeed) | ||||||||
| Multiply both sides by (r - 10)(r + 10) to get rid of the denominators, | ||||||||
| and simplify ... | ||||||||
|
|
||||||||
| So airspeed is about 124.29 miles per hour. | ||||||||
| Hmm, I don't think that these planes are F-16's. | ||||||||
| OK, now we look back at the original problem, | ||||||||
| and make sure we have actually answered | ||||||||
| what they were looking for. | ||||||||
| We have. | ||||||||
| They MIGHT have asked for something else, | ||||||||
| like the Time they have been flying, | ||||||||
| or the groundspeed of one or both planes. | ||||||||
| They didn't. | ||||||||
|
copyright 2005 Bruce Kirkpatrick |
