Ping Pong Analysis
My parabola for this video was based on a Ping-Pong hit. The hit was a positive parabola because the vertex was a maximum and the parabola starts low and shoots up in the air and comes back down. Because the distance travelled was very small, I used centimeter units for tracking the a, b, and c digits. The A digit stands for the width of your parabola. For instance my parabola was slightly narrow, so the A digit was -349.2 centimeters or around -3.5 meters. The C digit stands for the y-intercept of your parabola. For my y-intercept, I didn’t start at the height of the table, but a bit taller. So the C digit was placed at 25.59 centimeters, or around 0.26 meters. The B digit stands for the vertex, or the highest point of the parabola. The shot I made for Ping-Pong was fairly high; therefore, my vertex was pretty tall. My B digit was set at 263.9 centimeters, or around 2.64 meters.
If you were to put that all together in a quadratic equation – which is the equation we will be using to solve the parabolic motion – it would be easier to round up the unit of measurement to meters. Leaving us with the digits -3.5, 0.26, and 2.64. The equation would end up being y = -3.5(t2) + 2.64(t) + 0.26. In this equation we can sub in the time from any part of the equation and find out the y point.
In our daily lives, there are many different examples of parabolic motions. For example when you drink water from a water fountain, when the water comes out, it squirts in a parabolic motion. The y-intercept being where the water is erupting from, the vertex is when the water reaches the highest point, and the A digit being however wide the parabola of the water is. Another very common example of parabolic motions in our daily lives is throwing and catching a ball. The motion it makes when it leaves your hand all the way until it reaches the other persons hand is also a parabolic motion; however, most parabolas in our lives are restricted. A restricted graph means there is a start and stop that unlike other graphs do end.