Reckless+Dumping+of+Items+from+Overpasses

= Reckless Dumping of Items From Overpass =

**An Introduction**

 * A danger people often neglect to consider when driving is that hazardous activity comes from more than other drivers. The reckless throwing of things from overpasses is a terrible, and all too common, practice that is often thought to be trivial and ineffective but this page will show, with the assistance of kinematics, just how menacing this act can be. **

**Statistics and News Articles**
**Here are two stories of things being thrown from overpasses, two of the more heinous examples.**

"Dog Thrown From Overpass In Kalama." //Fox 12 Oregon//. 28 Jan 2008. Fox News, Web. 11 Dec 2009. <[]>.
 * A story of a man who threw his dog from an overpass.**

**The story of a man who threw his toddler from an overpass.** "Man Throws Toddler From Overpass." //11 Alive Atlanta, Georgia//. 18 Jan 2008. NBC, Web. 11 Dec 2009. <[]>.

**How Kinematics Applies**

 * For this particular scenario, kinematics is used in a slightly different sense than on the previous pages. Considering that an object is being released from an overpass, which goes over the road, we need to measure the velocity at which an object //drops// . The equations used are the same however; so do not let this change overwhelm you. **
 * For these scenarios we will look to understand what occurs during these overpass incidents using the physics principals we learned. We will need to calculate the position and along those lines the velocity and acceleration. Calculating these things will allow us to determine at what velocity the object would strike either a car or the street, how far it traveled, how long it took, as well as how much the object accelerated on its way down. If you take a look at the scenario below, you will see how we calculate the aforementioned concepts and if you can muster the strength to go farther down the page you can even learn how to use the concepts to //avoid// the falling objects. **


 * A young, happily married couple is driving on Interstate 95 late at night, enjoying the emptiness of the road. They are traveling at a constant speed at 29m/s and are approaching an overpass. The overpass is approximately 4.6 meters tall with their car, a mini cooper, being 140.7 centimeters tall. As they shorten the distance between their car and the overpass, they realize too late that there a kids holding a pumpkin over the edge poised to drop it. The pumpkin is dropped and breaks through the window traveling at an acceleration of 9.8m/s/s, the value of gravity on Earth. The pumpkin is dropped at second 6 and they begin to slow down at a constant velocity of 46.5m/s by second seven. Five seconds later, at second 12, they have reached a complete stop on the shoulder of the road. We are now going to use our skills to determine the kinematics behind the grievous event that just occurred and how we can use these same tools to help this happy couple avoid the incident ****. **



How To Solve
=== The first step in solving this problem is to identify what we know. We know the velocity is 29m/s, the overpass is 4.6m tall, the car is 140.7 cm tall, the pumpkin is traveling at 9.8m/s/s, the pumpkin hits window at second, the car starts to slow at second 7, the car comes to a complete stop at second 12, and the car slows down at 46.5m/s === === With the information provided we can use the concepts mentioned throughout the page to find out certain things about the car and driver. We can find out the velocity the car was traveling, how long it took the pumpkin to hit the car, the car’s acceleration (both positive and negative), and the total distance traveled. === === **The first thing, after the identification of relevant information, was to make a T-Chart. The T-Chart allowed us to see the distance traveled each second as well as the velocity. **On the left side of the T-Chart, we put seconds. We knew that the total time was 12 seconds. After putting this down, we looked and saw that we already had velocity. Velocity is the distance traveled over a specific time increment, in our case one. This meant for every second the car traveled however far, so for our scenario for every second the car traveled 29 meters. Knowing this allowed us to fill in the table by multiplying the number above the one you are filling by 29. (If I filling in the row with zero, I will multiply 29 by 1.) We have to do this because the car was not at a stop when we started taking time, meaning it had already traveled quite a bit. ===


 * **T(s) ** || **V(m/s) ** || **X(m) ** ||
 * **0 ** || **29 ** || **29 ** ||
 * **1 ** || **29 ** || **58 ** ||
 * **<span style="color: #808000; font-family: 'Arial','sans-serif'; font-size: 10pt;">2 ** || **<span style="color: #808000; font-family: 'Arial','sans-serif'; font-size: 10pt;">29 ** || **<span style="color: #808000; font-family: 'Arial','sans-serif'; font-size: 10pt;">87 ** ||
 * **<span style="color: #808000; font-family: 'Arial','sans-serif'; font-size: 10pt;">3 ** || **<span style="color: #808000; font-family: 'Arial','sans-serif'; font-size: 10pt;">29 ** || **<span style="color: #808000; font-family: 'Arial','sans-serif'; font-size: 10pt;">116 ** ||
 * **<span style="color: #808000; font-family: 'Arial','sans-serif'; font-size: 10pt;">4 ** || **<span style="color: #808000; font-family: 'Arial','sans-serif'; font-size: 10pt;">29 ** || **<span style="color: #808000; font-family: 'Arial','sans-serif'; font-size: 10pt;">145 ** ||
 * **<span style="color: #808000; font-family: 'Arial','sans-serif'; font-size: 10pt;">5 ** || **<span style="color: #808000; font-family: 'Arial','sans-serif'; font-size: 10pt;">29 ** || **<span style="color: #808000; font-family: 'Arial','sans-serif'; font-size: 10pt;">174 ** ||
 * **<span style="color: #808000; font-family: 'Arial','sans-serif'; font-size: 10pt;">6 ** || **<span style="color: #808000; font-family: 'Arial','sans-serif'; font-size: 10pt;">29 ** || **<span style="color: #808000; font-family: 'Arial','sans-serif'; font-size: 10pt;">203 ** ||


 * Now you might notice that this T-Chart only includes the first six seconds, the time before the great pumpkin debacle. Considering that the directions told us the car starts slowing down as second seven at a constant rate we now need to determine what that rate is in order to fill in the rest of that T-Chart. In order to find the position for each second during its’ slowing down process we did the same thing as above, considering this is only a contiunation of the aforementioned table. For this portion of the table we made it so second 6 was zero and proceeded to count up, you'll notice in the brackets next to the times you can see what the time actually is in relation to the rest of the project. **

<span style="color: #008080; font-family: 'Arial','sans-serif'; font-size: 10pt;">
 * **<span style="color: #808000; font-family: 'Arial','sans-serif'; font-size: 10pt;">T(s) ** || **<span style="color: #808000; font-family: 'Arial','sans-serif'; font-size: 10pt;">V(m/s) ** || **<span style="color: #808000; font-family: 'Arial','sans-serif'; font-size: 10pt;">Equation ** || **<span style="color: #808000; font-family: 'Arial','sans-serif'; font-size: 10pt;">X(m) ** ||
 * **<span style="color: #808000; font-family: 'Arial','sans-serif'; font-size: 10pt;">0[6] ** || **<span style="color: #808000; font-family: 'Arial','sans-serif'; font-size: 10pt;">46.5*0 ** || **<span style="color: #808000; font-family: 'Arial','sans-serif'; font-size: 10pt;">0+203 ** || **<span style="color: #808000; font-family: 'Arial','sans-serif'; font-size: 10pt;">203 ** ||
 * **<span style="color: #808000; font-family: 'Arial','sans-serif'; font-size: 10pt;">1[7] ** || **<span style="color: #808000; font-family: 'Arial','sans-serif'; font-size: 10pt;">46.5*1 ** || **<span style="color: #808000; font-family: 'Arial','sans-serif'; font-size: 10pt;">46.5+203 ** || **<span style="color: #808000; font-family: 'Arial','sans-serif'; font-size: 10pt;">249.5 ** ||
 * **<span style="color: #808000; font-family: 'Arial','sans-serif'; font-size: 10pt;">2[8] ** || **<span style="color: #808000; font-family: 'Arial','sans-serif'; font-size: 10pt;">46.5*2 ** || **<span style="color: #808000; font-family: 'Arial','sans-serif'; font-size: 10pt;">93+203 ** || **<span style="color: #808000; font-family: 'Arial','sans-serif'; font-size: 10pt;">293 ** ||
 * **<span style="color: #808000; font-family: 'Arial','sans-serif'; font-size: 10pt;">3[9] ** || **<span style="color: #808000; font-family: 'Arial','sans-serif'; font-size: 10pt;">46.5*3 ** || **<span style="color: #808000; font-family: 'Arial','sans-serif'; font-size: 10pt;">139.5+203 ** || **<span style="color: #808000; font-family: 'Arial','sans-serif'; font-size: 10pt;">342.5 ** ||
 * **<span style="color: #808000; font-family: 'Arial','sans-serif'; font-size: 10pt;">4[10] ** || **<span style="color: #808000; font-family: 'Arial','sans-serif'; font-size: 10pt;">46.5*4 ** || **<span style="color: #808000; font-family: 'Arial','sans-serif'; font-size: 10pt;">186+203 ** || **<span style="color: #808000; font-family: 'Arial','sans-serif'; font-size: 10pt;">389 ** ||
 * **<span style="color: #808000; font-family: 'Arial','sans-serif'; font-size: 10pt;">5[11] ** || **<span style="color: #808000; font-family: 'Arial','sans-serif'; font-size: 10pt;">46.5*5 ** || **<span style="color: #808000; font-family: 'Arial','sans-serif'; font-size: 10pt;">232.5+203 ** || **<span style="color: #808000; font-family: 'Arial','sans-serif'; font-size: 10pt;">435.5 ** ||
 * **<span style="color: #808000; font-family: 'Arial','sans-serif'; font-size: 10pt;">6[12] ** || **<span style="color: #808000; font-family: 'Arial','sans-serif'; font-size: 10pt;">46.5*6 ** || **<span style="color: #808000; font-family: 'Arial','sans-serif'; font-size: 10pt;">276+203 ** || **<span style="color: #808000; font-family: 'Arial','sans-serif'; font-size: 10pt;">479 ** ||
 * After we have completed the table, we have actually found quite a bit of information. We know the total distance the car traveled, 479 meters, as well as its velocity throughout. The two graphs below have illustrated these ovservations in a easy to read format.

Now that we understand the journey our car undertook we can start to work on the pumpkin. The first thing we are going to calculate is the total space the pumpkin had to travel in order to hit the car. We know that height of the overpass and the car, we simply need to subtract them from one another. You'll notice, however, that the height of the car is in centimeters, but fear not! The wonderful thing about the metric system is that a simple understanding of the number ten will get you all you need. In order to find how many meters are in 140.7 centimeters, we simply divide 100, this is due to the fact that there are 100 centimeters in a meter. That means that the car is 1.407 meters tall. Knowing this allows us to easily subtract the height of the car from that of the overpass, giving us a distance of 3.193 meters. Now let us continue... **
 * The equation, shown below, is one that at the present is solved for displacement. However, we already have displacement, therefore we are going to plug in what we know and solve for whatever we find we don't.**


 * The first thing we can plug in is acceleration, we know that the acceleration is 9.8m/s/s, due to the gravitational pull, allowing us to define 'a' in our equation. **
 * Next we can address the velocity issue, since velocity is neither applicable or necessary in this problem we can go ahead and remove that second portion of the problem. Now know that this is not a recommended practice, eliminating portions of a problem, but in this particular case we are alright. This leaves displacement, which we figured out above, meaning we can replace Δx with 3.139 and solve for t².**

**First we multiply 1/2 by 9.8 giving us 4.9, making our equation 4.9t****²=3.193. Next we divide each side by 4.9 equaling t²= (about) 0.65. This means you now need** **to find the square root of 0.65 which we shall simplify to 0.81. This means that it took 0.81 seconds for the pumpkin to crash into the cars' windshield .**

** Now An Abridged Version: **
-The car traveled at 29m/s -The pumpkin's velocity was 9.8m/s/s -It took 0.81 seconds for the pumpkin to break the windshield **
 * -Car traveled 439 meters in 12 seconds before coming to a stop



How Kinematics Can Help You Avoid Such Problems
However, as this site seeks to increase knowledge in all aspects we feel it is best to acknowledge that no one should be throwing anything off overpasses. It is an unsafe practice as shown by this scenario and sadly most do not end as happily as this one did. **
 * Now that we have gone through that long-winded explanation of the kinematics behind the accident you can use them to avoid these accidents in the future. For this particular scenario it is harder to offer advice in avoiding this accident being as you are not directly in control. We highly doubt that one deliberately drives into a falling object so the biggest piece of advice we offer it to stay observant. However, if you were to look at the kinematics solely to determine what to do, if you see the thrower and the object you can either accelerate or slow down to avoid the falling object. If you were to slow down or increase your speed upon seeing it, the object would accelerate a constant rate causing it to avoid the now slower or faster automobile.

**Conclusion**

 * As a driver you cannot hope to avoid every problem the world throws at you, you may not see the thrower on the overpass or the other driver approaching but that does not mean you cannot prepare yourself as best as possible. Let this page offer an example of one of life's unexpected "joys" and how you can use the tools you learn day in and day out to help best these troublesome accidents. If you simply take your time and think rationally there is always an easy way out. **