A nuclear weapon is an explosive device that derives its destructive force from nuclear reactions. Only 2 times in history has the nuclear bomb been used on civilians. Those 2 instances were in Hiroshima and Nagasaki at the end of WWII. It is our goal, as life preservers, to give you a better understanding of the nuclear bomb in a pre-calculative approach which may someday save your life.
There are several factors that influence the size of the resulting mushroom cloud. Explosive Quantity directly correlates with the apex and base of the mushroom cloud. This lesson will allocate all of the quintessential mathematical relevancies in order to predict the size and destructive pattern of a nuclear bomb.
EXPLANATION The previous graph used an exponential equation to model the height of numerous mushroom clouds. However, their scale did not accurately truly depict the size. So, we created our own power function in order to fix the mistakes of our online counterparts. As we know it, this is the only graph in the world that predicts the height of a mushroom cloud based on terms of kilotons.
Step by Step Partition 1.Enter in L 1 the variations in kiloton quantity. 2. Enter in L 2 the corresponding height of mushroom clouds. 3.Enter in L 3 the base height of the mushroom clouds. 4.Use power regression feature to determine the graph made by L 1 & L 2 and conversely for L 1 & L 3.
Step by Step Partition Cont. 5. Use the vars feature to copy and paste the derived functions into y 1 & y 2. 6. Ensure that the stat plots are turned on so that the graphs will appear. 7. This graph is so boss that any normal window will not fit it so we created our own window. (Xmin=0 Xmax=50000 Xscale=3000 Ymin=0 Ymax=150 Yscale=25)
SCALE & FINAL EQUATION The Xscale is in kilotons which is 1000 tons. The Yscale is in feet but at a scale of 1000. Y=11.397X^0.237 (TOP OF CLOUD) Y=5.692X^0.262 (BOTTOM OF CLOUD)
Problems You Can Do With these equations you can easily estimate the height and base of a mushroom cloud If you want to fly over a cloud made by a 25 Megaton(25000KT) bomb, at least how high should you fly? Using the trace feature of the calculator, by entering 25000 you will find the estimated height to be 125.724(1000)Ft. High You would have to fly at least 23.811 miles high to avoid the cloud
Nuke Area In order to calculate the area the bomb will directly annihilate, there are two relative equations. With an expanding radius, the area will be determined by the linear equation of the radius. The equation of the radius is linear, represented by y=.5x, where it is measured in miles per second. The area of the circle is represented by y= πr^2, but since the radius is y=.5x the final equation for the area of the circle is y=π(.5x)^2. The fireball of a nuclear bomb dissipates after 40 seconds, therefore that is what we will plug in for x. y=π(.5(40))^2 = 628.319 square miles.
STORY During 2014, Kim Jong Il, dictator of North Korea, is planning a world takeover. He has pioneered the largest North Korean bomb ever, the F-bomb. Measured at 25 megatons, his first target is Neshannock High School. Because Anthony and Jono have modeled the destructive patterns of the nuke, we will be able to provide you with information critical to your survival.
SURVIVAL Due to the bomb’s explosive power. You first need to find the height and the area of the nuclear fireball of doom. We discovered earlier in the slideshow that the height was about 24 miles high and the radius was about 30 miles. So, in order to survive this North Korean Tragedy, you must be either 30 miles away or 24 miles in the sky.
WORKS CITED http://www.carloslabs.com/node/16 http://dgely.com/Bikini/Nuclear%20Testing /Tsar%20Bomba/Tsar%20Bomba.htm http://www.nationalterroralert.com/nuclear/ http://en.wikipedia.org/wiki/Mushroom_clo ud