weaks4_5

Room 56

Weaks

Period 4 INTEL ii GENCE Jimmy: Math Cruncher Anthonie: Recorder/Facilitator Esteban: Facilitator/Recorder Michael: Math Cruncher

follow the directions on the Vertical Motion page, to complete each of the sections below.
===You are standing on a bridge over a creek holding a stone 20 feet above the water. You release the stone. How long will it take for the stone to reach the water? ===
 * __The Word Problem__:** How would you solve for time in the problem your group was assigned? Prepare the equation to solve for time, defining the variables and supporting your choice in equation.

This equation is the correct equation because the object is dropped not thrown and the measurement is in feet not meters.

h = the height of the object at any given point in time. -to measure how high the bridge is t = time the object is in motion -how long the object is in the air = the initial height from which the stone was dropped or launched -the staring height of the object in the equation

Standard Form:


 * __The Parabola:__** Use what you know about parabolas to predict the shape of the graph. What will it look like, and how do you know?

a=-16 b=0 c=20

Because A is -16 then the parabola will be a maximum, meaning that it will open downward. The magnitude has to do with the width of the parabola. Our parabola will be skinny, because the magnitude is at the 20 range. The variable 'c' determines the y-intercept, because on the graph the parabola crosses the y-intercept at positive 20.

The discriminant is the part of the quadratic equation in the square root. To solve the discriminant you need to:


 * 1) Determine the variables
 * 2) Solve the exponent
 * 3) Multiply 4, 'a,' and 'c'
 * 4) Add


 * The solution to the discriminant is a po****sitive 1280, and the discriminant determines the number of roots so we know there will two roots on the X Axis.**

that they mean for the problem you were given.
 * __The Math__:** Pretend you are the teacher, and this section is your lesson. Post the calculations required to graph the equation and find the solution, and show all the steps to doing so. Teach your audience all the important parts of the graph and explain

**To find the Axis of Symmetry:**

 * 1) Use the formula -b/2a
 * 2) Determine the variables
 * 3) Plug in the variables
 * 4) Multiply
 * 5) Divide
 * 6) The answer will be used as the line on the graph were the parabola will be centered

To find the Vertex:

 * 1) Plug in the A.O.S. to the 't'
 * 2) Multiply
 * 3) Add
 * 4) The answer will be used as the starting point of the parabola on the AOS

[[image:Graphy23.png width="329" height="331"]]
The axis of symmetry for our equation was 0, and then we used the Axis to find the vertex which was 20.

The best way to solve for 'x' for equation would be to use the quadratic equation, because factoring would not work in our case. After determining the variables and solving the quadratic equation it is easy to graph and to find the solution.


 * __The Soluti__****__on and The Meaning__:** What do the different parts of the graph mean? What does the solution mean?

[[image:Solution443.png width="192" height="149"]]
-The solution to our vertical motion problem signifies how long the object took to hit the water, which was about 1.12 seconds because you can't go back in time. -The vertex represents the point where the object is dropped, because the vertex is the highest point where the stone is dropped, which is at the coordinate (0,20). Zero represents the starting time and 20 represents the starting height. -The y-intercept represent height from which the object was dropped. -The roots represent the place where the object hits, but only one solution can be correct because you can't go back in time. -The object is in air 1.12 seconds, and we know this because when the object was dropped it took 1.12 seconds from 0 to get to the roots. Also, because we can't go back in time.


 * __Reflection__** How did it feel to do the work and pretend to be the teacher? Do you think you understand the material more, now? Why or why not?

__**Michael:**__ One thing I found to difficult to do was to use so many different programs. To make the project run smoother I would recommend using less programs. Doing this project did help me understand the vertical motion and quadratic equations, because all the hands on work helped me understand how to use all the formulas. Being the teacher was difficult, because we had to explain everything very thoroughly.

__**Esteban:**__ The math was the most difficult part, because we didn't touch upon it. To make the project run smoother next time I would use a calculator. Doing this project did help me understand the vertical motion and quadratic equation, because it helped me with the steps. Being the teacher really helped me understand vertical motion, and now I feel much better.


 * __Jimmy:__** This project was easy when the whole team worked together. The most difficult part was the math, because we did not know every part of the formulas but we figured it out. To make this project run smoother next time I would use a calculator. Yes, I do understand the vertical motion and quadratic equation better because I know the formulas better. Being the teacher was rather easy.


 * __Anthonie:__** I found the math to be the most difficult, because of the quadratic formula. Next time to make the project easier I would use any kind of tool that would help me with math. This project didn't really help me, because I still find the formulas and equations are still a little confusing. Even though the project wasn't the best helpful, I still got some things out of it. I felt good about pretending to be the teacher, because my group and I got to work and work well together and we know how to explain things so we all can understand it.