Linear Equations Lab Report

In this lab we will explain how to deduce the equation landing position of the ball thrown by the robotic arm stand. We must create the equations in terms of the radius, height, arm rotation speed, and release angle. The equations must be made with those variables because, those variables are what can change where the ball will land in the cup, and will make the equation more useful to the client. To make sure the equation will remain accurate we have to keep track of all the units throughout the process. Knowing that all equations should be solved in terms of the variables we can create an equation according to those variables starting with time.

Since k equals the rotations per minute k will be the measurement of radians divided by the time it takes for the arm to arrive at that radian. The angular postion of an equation is therefore equal to 2*pi*k*t+ initial angular position. Since we also know that time and radians both equal zero initially, we determine that the angular position, which we will call @t, equals (2pi)*k*t. The variable t stands for time and 2pi is multiplied by k to represent that k is in term of rotations.

Next, we move on to finding the …show more content…
The usual equations to find the x and y position equations are as follows: position-x= mx+b and position-y= g/2(x^2)+vel(x)+in. M equals the slope of an equation which can be found by taking the derivative of the x equation, which we have done, and vel represents the velocity of the equation. g/2 represents the acceleration affecting the equation, which is gravity, and in represents the distance from the vertex to the origin. Notice that gravity had to be converted in order to keep all units consistent throughout the equation, shown in work. After plugging in the appropriate information, shown on work, we find the position x and position y equations. The position x will be called PX(t) and the position y equation will be called