At first when Mrs. Mariner asked us where we use math in secret, my mind went blank. To be honest, I really enjoy math, but the whole "apply what you learn" thing, doesn't usually cross my mind when I am going on about life. I wish I thought that way, but I'm not THAT smart (; After these thoughts finished crossing my mind, I thought about the question again.
Somewhere that I definitely use math or see math being used, is in ski racing. I ski race on a competitive ski team that competes at United States Ski Association races. For my age group, there are certain rules that MUST be followed for these races. One of the things that is important when choosing a ski that will fit the requirements and provide you maximum success, is the turn radius of the ski.
For example, for slalom, you do not want to have a ski with a too turn radius. In slalom, the gates are closer together and you want to make tighter, quicker turns. Therefore, you have to make sure that the slalom ski you purchase has the right sized turn radius. Contrary to a small turn radius, for Giant Slalom, you can have a ski with a smaller turn radius. Giant Slalom is just what it sounds like it is. The gates are much farther apart than in slalom and you have more time to make larger turns.
Turn radii are very important in ski racing. This is a way that math applies to my life that I had not recognized until now. It is kind of cool to see that something I am so passionate about has math involved in many ways, one of those being what I just talked about.
Monday, September 23, 2013
Friday, September 6, 2013
Grades and Slopes
To be honest, when I read Ms. Mariner's 9% grade post, I wasn't sure where to even remotely begin my own post. Even when she offered for us to write about the triples, I was stumped. When reading the math illiteracy post, I almost immediately could think of a creative way to respond. The 9% post however, was the opposite experience. That's okay though, because it is good to have to think about things!
Before reading the post, I would have never thought that the grade of hills, ramps, or roads could be a "discussion topic." It is something that I never really put any thought into whatsoever! However, once you get your mind thinking, it is a very important aspect of building things such as ramps and roads. If the grade of a road is too high, cars will not be able to safely make it up and down the road. If the grade of a ramp, particularly for disabilities, is too high, people that are originally trying to have easier access to wherever they are trying to go, cannot make it up the ramp.
In relation to trigonometry, grade is very similar. Specifically, the angle of elevation is a huge factor. The angle of elevation is something that, using trigonometry, we can somewhat easily solve for when provided with the proper information. Angle of elevation is a large factor in grade because it is how much the new slope is "raised up," from the previous ground level.
In this picture from the wikipedia site that Ms. Mariner directed us to, you can see that a trigonometrical function that comes into play is the tangent (opposite divided by adjacent). If you know the angle of elevation and one of the legs, you can solve for the other leg.
http://en.wikipedia.org/wiki/File:Grade_dimension.svg
In the picture, grade is presented as a right triangle. Woah! That's what we are studying! Hmm. Could that maybe, possibly have to do with anything at all?
In the picture, the road is the hypotenuse of the right triangle. The previous ground level is one leg, and the distance from the previous ground level to the slope is the other leg. We can use the tangent to find the length of the hypotenuse, thus finding how much the slope increases (or decreases depending on your perspective), in a certain distance.
Grades are an interesting topic that I had never put much thought into before, but I am glad that I had the opportunity to now!
Before reading the post, I would have never thought that the grade of hills, ramps, or roads could be a "discussion topic." It is something that I never really put any thought into whatsoever! However, once you get your mind thinking, it is a very important aspect of building things such as ramps and roads. If the grade of a road is too high, cars will not be able to safely make it up and down the road. If the grade of a ramp, particularly for disabilities, is too high, people that are originally trying to have easier access to wherever they are trying to go, cannot make it up the ramp.
In relation to trigonometry, grade is very similar. Specifically, the angle of elevation is a huge factor. The angle of elevation is something that, using trigonometry, we can somewhat easily solve for when provided with the proper information. Angle of elevation is a large factor in grade because it is how much the new slope is "raised up," from the previous ground level.
In this picture from the wikipedia site that Ms. Mariner directed us to, you can see that a trigonometrical function that comes into play is the tangent (opposite divided by adjacent). If you know the angle of elevation and one of the legs, you can solve for the other leg.
http://en.wikipedia.org/wiki/File:Grade_dimension.svg
In the picture, grade is presented as a right triangle. Woah! That's what we are studying! Hmm. Could that maybe, possibly have to do with anything at all?
In the picture, the road is the hypotenuse of the right triangle. The previous ground level is one leg, and the distance from the previous ground level to the slope is the other leg. We can use the tangent to find the length of the hypotenuse, thus finding how much the slope increases (or decreases depending on your perspective), in a certain distance.
Grades are an interesting topic that I had never put much thought into before, but I am glad that I had the opportunity to now!
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