weaks5_8

Weaks Period 5 Group 8

Team Name: Cake>Pi (3.141592653589793238462643383279502884197169399375105820974944592307...) Recorder - King Diaz Number Cruncher  - Lincoln To Facilitator  - Alejandro Martinez

Follow the directions on the Vertical Motion page, to complete each of the sections below.
A gymnast dismounts the uneven parallel bars at a height of 8 feet with an initial upward velocity of 8 feet per second. How many seconds will take him to reach the ground?
 * __//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.

We know we use this equation and this information because it was thrown upwards so it has an initial velocity, and we want to see how long it takes the gymnast to reach the ground from a height of 8 feet. We know 8 is positive because the object was thrown upwards, not downwards.

h=The height of the object at any given point in time. Will be 0 because we want the gymnast to reach the ground. t=Time the object is in motion. This is the time it takes for the gymnast to reach the ground. h subzero=The initial height the object was dropped or launched at. In this case, 8, for 8 feet high. v=The initial velocity (ft/s) of the object when launched. In this case, 8 ft/s thrown upwards.



a=-16 to factor in gravity for the equation. b=8 because the gymnast was launched upwards at 8 feet per second. c=8 because the gymnast's initial height was 8 feet.
 * //__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?

Since a is negative, it will make the parabola open downwards, and since it is 16, it will be a thin parabola. If a was positive, the parabola would open upwards and if it was a number closer to 0, or a fraction, then the parabola would be wider.

c determines the y-intercept of the parabola, which will be +8 in this equation. The y-intercept is where the line crosses the graph, and the line will cross at (0,8). This is the starting point of the gymnast, which is 8 feet high.

To start, we have to find the discriminant to know how many roots there are. If the answer to the expression below is positive, there are 2 roots. If it is negative, then there are 0 roots. If the answer is exactly 0, then there is 1 root.



Since the discriminant is positive, that means that there will be 2 roots for this parabola. A root is the x-intercept of the parabola, or the solution.

We need to start off with finding the axis of symmetry so we can find the vertex. The AoS is the line that divides the parabola down the middle. Axis of Symmetry: To start, we have to find the axis of symmetry using. 8 is the value for b, and -16 is the value for a, so we plug those in to the corresponding spots. That simplifies into -8 over -32. When simplified, that turns into 0.25. This is the x-value of the vertex, and the axis of symmetry. Vertex: To find the y value of the vertex, we need to plug in the AoS, which is 0.25 into the equation.
 * __//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 what they mean for the problem you were given.

0.25 squared is 0.0625. One fourth of 8 is 2, and 8 stays the same. -16 times 0.0625 is -1, and the other values stay the same. Simplified, the equation ends at y=9. The x-value of the vertex is 0.25, and the y-value is 9. The vertex is above. This is the graph of the parabola for this equation. The roots represent the solutions to the equation, which is the time for the gymnast to reach the ground. Since the answer cannot be negative, because you can't take a negative amount of time to fall, the negative answer is eliminated. The y-intercept is the starting point of the gymnast.

We decided to use the quadratic formula because we found that it would probably be easier than factoring or completing the square, and it is a straightforward process.

To start, write out the quadratic formula. After plugging in all the values, the formula should appear like this. -4 times -16 times 8 turns into 576, while 2 times -16 turns into negative 32. The square root of 576 is 24, so the square root of 576 turns into 24. Since the expression says plus or minus, the expression is changed to have plus or minus. Simplify that. == The answers here, 0.5 and 1, match the answers on the graph, which are the roots. Since it can't take a negative amount of time to fall, 1 would be the answer.

The solution, which is one, means that the gymnast would take one second to reach the ground. Since the solution can't be negative, because it can't take a negative amount of time to fall, -0.5 can't be the answer.
 * __//The Solution and The Meaning//__: ** What do the different parts of the graph mean? What does the solution mean?

The vertex represents the highest point that the gymnast reaches. Since the gymnast was propelled upwards, that means that the gymnast has to move farther up before reaching the ground. 0.25 represents the time taken for that height, which is 9 feet high, or the y-value of the vertex.

The y-intercept represents the starting point of the gymnast, which is 8 feet high. This is because "c" is the height of the gymnast at any point in time in this equation, and we need to see how long it will take for the gymnast to reach the ground after being propelled off of a bar 8 feet high.

The roots are the solution of the problem, which is how long the gymnast would take to reach the ground. Since the answer can't be in negative time, the answer would have to be 1. The roots in any parabola represent the solution, and the solution in this case is the time taken to reach the ground.

The object, which was the gymnast, was in the air for one second. We know this because the solution is 1, and the question asks how long will the gymnast take to reach the ground. The time taken to reach the ground after being propelled is the time spent in the air.

** __//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

Lincoln:
= The main thing I found difficult about this project was explaining how to do everything. It was hard to find a way to explain it so that everyone would be able to understand what was happening, instead of just seeing a lot of numbers. If anything, I would probably want everyone in my group to have a computer, instead of just one person working on it and the other people doing things on paper. This is because everyone could be doing something to benefit the project on the wiki. This project was good for helping understand quadratic equations and vertical motion because it gives you an example of how this is applied to life. Pretending to be the teacher was actually nice because you could choose what to do, and how to do it. =

=**King: I found the equation for vertical motion with an initial velocity very confusing. Also, solving it with the plug-in number. Having a much more simpler project would make the project smoother for me next time. Yes, the project helped me understand vertical motion better because it compared the problem into reality instead of just saying a=a, b=b, and c=c. Actually, Lincoln was like the leader of the group because he knew more information than me and the facilitator. **= =Alejandro:= = T**he one thing I found difficult is the roots because I thought they were wrong. Our project went real good and we finished with some days extra. Now I understand the project because when Lincoln explained it, it made sense and I understood it. What I found difficult was explaining it so the people will understand it when we present the project.** =