Reckless+Dumping+Of+Items+From+Overpasses

= **Reckless Dumping of Items From Overpasses.** =

== Background Information: ==

There have been many cases where teenagers dump things such as rocks over overpasses which cause extreme damage to not only the car but also the people in it. In 1999 a Canadian teenager was driving along the highway when a rock smashed into a SUV. He suffered from permanent brain damage from this reckless event that could have been avoided if people made better choices and used their better judgment. [|WRAL.com] = Scenario: = While Bob was driving down the Vine Street Expressway towards Center City, little did he know there were some juveniles thought it would be funny to drop a bag with a half eaten burger inside of it off the overpass that Bob was quickly approaching. He was traveling at 30m/s and when they dropped the bag it was a direct hit on his windshield. There was smeared burger everywhere all over his windshield and he decided to go to a car wash but first he has to pick up his son.

Question:
How far away was Bob from the overpass for the bag to have hit him directly in the windshield?

__ What We Know: __
**Overpass Size:** About 16 Ft. Clearance (About 5 meters) + 4 foot bridge thickness (About 1 meter) = 6 meters []

Acceleration: 9m/s/s The bag fell at about 9m/s/s as it fell off the 5 meter overpass.
 * Bag Information:**

Rate of travel: 30m/s The Mazda is traveling towards the overpass
 * Car Information:**

Standard Form Equation:
In this equation.

x = the position a = the acceleration t =time v = velocity *anything with a subscript of 0 means that it's that term at the starting point.

** Problem Breakdown: **
Bag Calculations

According to NASA, a free falling object will fall at an acceleration rate of 9.8m/s/s when there is no air friction. Using a graph, finding the position is like like finding the area of a triangle when the velocity is known. The **slope** of this graph describes the acceleration of the object which is 9.8m/s/s

Using this information we can find the average velocity for each time interval usin the formula...

Using the formula for position we can use the acceleration to determine the position of the bag during each second

Using this formula, we can fill in for the acceleration which is 9.8 and the time for the first second which is 1, squared This equals 9.8 and we are left with the half. Half of 9.8 is 4.9 which is then the position of the bag at 1 second

In order to find how long it will take for the bag to fall 6 meters, we can fill in what we know into the equation.

So in about 1 and a half seconds the bag travels the length of the bridge which is about 6 seconds

Car Calculations:
For the car, we know that is it traveling down the highway at 30m/s which is the velocity of the car. Using the same equation used for finding the velocity of the bag, we can find the acceleration using what we know about the velocity of the car. Using this formula, we can fill in what we known and solve for what we don't know.



Knowing that the car will travel 30 meters in one second then we can assume that it was about 30 meters away from where the bag was dropped off the bridge. This is because we know that the bag traveled about 5 meters in 1 second and 6 meters in about 1 and a half seconds which is the length of the bridge. Knowing these two things we can assume that in ta little more than 1 second of time, the car was about 30 meters away and that's why the bag hit the windshield directly.

Motion Map:


In this motion map, the 0 stands for the origin where the bag and the car would meet. The car starts at about 30 meters away and moves towards the origin and intersects it in about 1 second. For the bag, when it starts at 4.9 meters away, in 1 second it intersects the origin. This shows that the bag and the car would intersect in a little bit over a second because of the fact that the overpass is about 1 meter larger than what is represented.

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