Physics Journal #5

This week we expanded on projectile motion problems. These are quite a bit different from Horizontal projectile problem because angles are being involved now. The angles being introduced brings with it the use of vector triangles. you use vector triangles to figure out the velocity of the “X” and “Y” in your “X Y Table”. This is a very important idea to grasp because it is a common mistake to use the hypotenuse of the vector triangle as the Velocity in both of the “X” and “Y”. Problems using projectile motion at an angle with also be on future assessments.

Physics Journal #4

This week in Physics we talked about Horizontal Projection. In order to solve problems with horizontal projection, you will need to create an “X Y table”. This is because in order to find what you are looking for you need to separate the 2-d Kinematic problem into 2 different 1-d equations and solve. In the “X Y table” you put all the information that you are given and try to figure out which equation to use in order to find the answer. This is a very important concept to understand because you will need a firm grip on how to do these problems in order to be able to do Projectile problems at an angle.

Chapter 1 Closure

Equation

1. Table – A table is a list of inputs and outputs that go with the equation.
2. Domain – The domain sets restrictions on the inputs that go with the equation and is also a list of “x” variables that work with the equation
3. Range – The range sets restrictions on the outputs of an equation and is a list of the “y” variables of an equation
4. Graph – A graph is a visual representation of what points on a coordinate plane are apart of the equation. Both a table and a graph are multiple representations of the same thing, which is the equation.
5. Slope – The slope is apart of an equation and is being applied to the “x” variable. The slope can also be found on the graph by counting the change in the y and x in a graph, usually expressed as the phrase as “Rise over Run” and mathematically phrased as change in “y” as change in “x”.
6. Function – A function is another name for an equation.
7. Inverse Function – A function is another name for an equation. An Inverse Function, like it is named as, is an inverse of a function. Ex: a squared equation’s inverse is a square root equation.

Inverse Functions

Write a Learning Log entry that demonstrates what you have learned about inverse functions. If you have a function and its inverse, how can you be sure that both equations represent functions? How can you verify that the functions are inverses of each other? Include an example by selecting a function and its inverse and then justifying that the functions are inverses of each other. Use multiple representations and function composition. Do you have to restrict the domains of your functions? 

If you are given a function and its inverse you can input one function into the other one then see if it ends up with “y = x”. Also if you want to see if a functions’ inverse is actually a function you can see if the original one passes the horizontal line test. This is because since the inverse is a reflected function the horizontal line test becomes the vertical line test. In the example below, the one on the left, you are trying to solve for the inverse. the first step is to swap the “x” and the “y” and then solve for the “y”. And then in the example below, the one on the right, you will reflect the original function over the identity line, which is “y = x”. They reflected it wrong however in the one below because it is currently not a function. in order to make the inverse an actual function, you need to restrict the domain and range.

Physics Journal #3

A very important thing in physics is the concept of gravity in free fall questions. In most cases, gravity in a free falling question is 9.8 m/s^2, which is the gravity on earth. Gravity takes place as the acceleration in the equation that you are solving. This is because an object from freefall is accelerating at a pace of 9.8 m/s^2 because of gravity pulling the object down. This is important to know because when you are asked a free fall question on the AP exam or any tests you will have to know that gravity is inputted in for acceleration.

Physics Journal #2

There are 7 basic equations that we should memorize for this class. Them being pictured below. In Physics it is very important to know the very simple things so it is imperative to know these equations and understand which ones to use. In order to find which equation to use for each instance. In order for you to find this out, you have to find what variable you are solving for and what is the missing variable. For example, in order to find the distance you have to figure out what the missing variable is, it is either acceleration or final velocity.

PreCalc Eportfolio #1

“What challenges did you encounter today and how were you able to overcome those challenges?”

The main challenge that I encountered today and Friday was how to find the area of each line for the course. Me and my partner Emery where able to overcome this by using specific equations for the lines, for the Parabola shaped line we used the equation for an oval and divided it by 2 since it was only half of an oval. We did a similar thing for the curved line but divided it by 4 instead of 2. Another challenge that my Partner and I faced was how to decide how to get the lowest amount of money for the dirt bike course to cost. Emery and I went through a multitude of mock course that could give us the course that would allow us to save the most money. The order that we decided on our course was to have the absolute value equation first, parabola second, square root function third, and The wavey one (couldn’t think of a proper name) last. This particular course gave us the grand total of the project being $55.37. The way we overcame this obstacle was by looking at and learning from other groups to see what they did to get a lower amount.

Physics Journal week 1

 

One of the most important things we learned this week was about accuracy and Precision. Accuracy is the measure of how close you are to your theoretical, which is your goal, and Precision is the consistency of your data. The big topic that was discussed was that you can be accurate and not precise and vice versa. We also learned about to types of error that can affect our experiments. The first type is Random error is when there is neither accuracy or precision. the second type is systematic error, this is when it is not accurate, but it is precise. With systematic error, you are also able to identify what is making your data not accurate.