You are a physics student conducting an experiment on gravity by dropping an object from a great height. You stand at the top of a lighthouse that is 200 feet tall. The base of the lighthouse is an additional 300 feet above the ocean below, and you have a clear shot to the water below to examine the claim regarding vertical motion made by Galileo But, this being the 21st century, you have access to a sophisticated laser tracker that continually tracks the exact height of the dropped object from the ground as well as the length of time elapsed from the drop. At the end of the trial, you get sample data in the form of a table. You examine the data and determine the relationship between time and height. Negative values represent when the object passes the base of the lighthouse. . . For this performance Task, use these definitions to make sense of the problem and to calculate your final answers. Galileo: an Italian scientist and scholar who made pioneering observations that laid the foundation for modern physics and astronomy Laser Tracker: measures 3-D coordinates (i.e. height) by tracking a laser beam to a retro-reflective target held in contact with the object of interest Projectile: a projectile is any object that once projected or dropped continues in motion by its own inertia and is influenced only by the downward force of gravity. . Galileo performed experiments on projectile motion and sought to determine the path of a projectile. He was able to determine that the path of a projectile is parabolic and claimed that a falling body would accelerate downward at a uniform rate (i.e. the second differences of its height as it falls are constant.) You simulate Galileo's experimentation and obtain the following data: Time 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Height 200 196 184 164 136 100 56 4 -56 - 124 -200 1. To answer questions 1-4, complete the Difference and Ratio table on the next page. (3 points) a. Calculate the difference in y-values (first differences) over each equal interval. b. Calculate the first and second