Earthquake! - May 6-10, 1996
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I was hanging out in the Seattle area, staying with my friend Steve who lives near Duvall, Washington, about 30 miles north and east of Seattle. Thursday night we got back to his house, and there was stuff all over the floor. Steve says jokingly, "Looks like we had an earthquake!"Thirty seconds later the phone rings, and it's his friend Jim asking how we enjoyed the earthquake. So there really was an earthquake of magnitude 5.4, and it turns out the epicenter was really close to Steve's house!
We didn't actually feel the initial quake because we were in the car, but there were a few really cool aftershocks that night, and a really good one Saturday morning that rocked the house again (magnitude 3.6) and woke both of us up.
The epicenter was 6.3 miles ENE of Duvall. Steve lives 7 miles ENE of Duvall. The earthquake happened 5 miles underground (under the epicenter - the "epicenter" is the place on the surface directly above the earthquake). How far is Steve's house from the epicenter, and how far is his house from the actual location of the earthquake?
If you want to know more about the earthquake, the University of Washington has a special page up atExtra Tough Research Project: What was the magnitude of the quake by the time it got to Steve's house? (You have to figure out how much the force of the quake diminishes as it gets further from the epicenter.) Here's some more information:http://www.geophys.washington.edu/SEIS/EQ_Special/Duvall/
- there are even maps, and you can see where I was (under all the aftershocks!).
Steve's Latitude 47 degrees 46 minutes 16 seconds Longitude 121 degrees 53 minutes 49 seconds Epicenter Latitude 47 degrees 45 minutes 36 seconds Longitude 121 degrees 51 minutes 00 seconds 3.6 Magn. Latitude 47 degrees 45 minutes 36 seconds Aftershock Longitude 121 degrees 52 minutes 48 seconds
Annie says: Solutions
This wasn't an exceptionally difficult problem, as evidenced by the 43 right answers I got. Content-wise it was more suited to the beginning of the year, but I just couldn't pass up the chance to tell y'all about the earthquake!
Most people used the Pythagorean theorem to solve the problem, though there were a couple who used trig. When a problem is this simple, it's a good opportunity to provide a good explanation.
No one has produced anything on the extra research part, though Amy Forster made some noises about looking into it. We'll see how that goes - maybe I will save it for a problem for next year.
Following are some highlighted solutions. The names of all the people who submitted correct solutions and most of the solutions are also available.
Jason Yeung Grade: 9 School: Iolani School Answer: The epicenter is .7 miles from Steve's house. The distance between the house and the actual spot is the square root of 2549 and all over 10. The actual spot, epicenter, and Steve's house form a right triangle like this. Steve's house .7 miles epicenter __________________ \ |_| \ | \ | \ | \ | \ | \ | \ | 5 miles underground \ | \ | the distance we are finding \ | \ | \ | \ | \ | \ | \ | \| actual spot Therefore, to solve the second part of this question, I can use the Pythagorean theorem. 2 2 2 a + b = c So the answer is .7 square plus 5 square is c square. 2 25.49 is c So the answer is the square root of 25.49 miles, or approximately 5.0489976 miles. For the first part, I just subtracted 6.3 miles from 7 miles and got .7 miles because they are on the same direction.
Amy Forster Age 11, Grade 7, Homeschooled Wilkins/Forster family Crooked Tree Point Cygnet, Tasmania, Australia. Answer: 1. Steve's house is 0.7 miles from the epicentre. 2. Steve's house is 5.05 miles away from the actual spot of the earthquake. Solution: 1. Steve's house is 7 miles - 6.3 miles = 0.7 miles from the epicentre. 2. I formed a triangle with a right angle at the epicenter, and joined the epicenter, Steve's place, and the actual center of the earthquake, as vertices. Using Pythagoras' Theorem, distance of Steve's house from actual center ^2 = distance from Steve's to epicentre^2 + distance of epicentre to actual centre^2 = 0.7^2 + 5 ^2 = 25.49^2 So distance of Steve's house from actual center = sqrt25.49 = 5.05 miles I am interested in finding out what the magnitude of the quake was by the time it got to Steve's house. I think I will need to know what force a 5.4 magnitude quake has. I think it must be terrifying to live in your part of the world where there are so many earthquakes. I hope Steve has a peaceful summer!
Cassie Gorish Grade: 8 School: Murray Middle School Well, the first part was easy.r7 - 6.3 = .7 - so Steve lives .7 miles away from the epicenter. The second part uses the Pythagorean Theorem. ____.7____H | / 5 | / | / | / | / X | / | / | / | / |/ E Point H is where Steve's house is. Point E is where the earthquake actually occurred. X is the distance from point E and point H. Here comes the Pythagorean Theorem: (Length of Leg 1)squared + (Length of Leg 2)squared = (Length of Hypotenuse)squared 5 squared + .7 squared = Hyp squared 25 + .49 = Hyp squared 25.49 = Hyp squared Approximately 5.049 = Hypotenuse So Steve's house is approximately 5.049 miles away from the place where the earthquake actually occurred.
Sean Mackaay and Conor Stokes Year 9, Age 13 South Fremantle Senior High School Western Australia First we must redefine the question. How far is Steve's house from the epicenter and how far is his house from the actual earthquake to a sensible accuracy. To start we look at the information given to us. Steve lives near Duval, Washington. This is about 30 miles north and east of Seattle where the person doing this article is living. The above information is quite useless when it comes to the actual question but it does set the scene and it tells us where Duval is. Steve lives 7 miles ENE of Duval, the epicenter was 6.3 miles ENE of Duval and the actual earthquake was 5 miles underground. This is quite important because saying that Steve lives 7 miles out of Duval and the epicenter was 6.3 miles out of Duval does not mean that they are on the same bearing. However they are on the same bearing (ENE) and as such it is quite simple to work out how far from the epicenter Steve's house is. We take 6.3 from 7 and we get 0.7 miles. With this information we can start to construct a model (See diagram.)This model is a right angle triangle and we know what a and b equal but now we must work out what the hypotenuse or h equals. To do this we will use Pythagoras's rule. This rule is that h2 = a2 + b2 or h equals the square root of a2 +b2. So a2 is 25 and b2 is 0.49. We add these together and we get 25.49 so we can update our equation of h2 = a2+b2, we now have h2 = 25.49. So we must find the square root of 25.49. This is a simple process in this day in age, just take out the old calculator, punch in a couple of numbers and we have the answer of 5.0486762225. We could just give this as the answer and be done with it; however this is much too accurate for the example. In the problem the numbers are given quite roughly and the most accurate it gets is to 1 decimal place (the epicenter was 6.3 miles from Duval). To show this we will break down the answer: the answer was 5.0486762225. This is 5 miles, 48 metres, 67 centimetres, 2 millimetres and 225 micro metres. This is ridiculous, so we get rid of the micrometres to start with. This is still ridiculous, so we have to get the number to 1 decimal place, so it coincides with the most accurate number used in the problem. If we do this we get 5.0 miles; this is not accurate enough, however, because the side must be more than 5 miles because side a is 5 miles long. So we go to 2 decimal places and we get 5.05 miles, which is more suitable, and this is our answer as accurately as is possible.
Carolyn DiMaria Mt. St. Joseph Academy, Flourtown, PA
Josh Hersh Grade 8 Georgetown Day School, Washington, DC
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