#Gravity experiment
The rate of acceleration of an object that is dropped varies between 9.76ms−2 and 9.83ms−2 depending on location. At Auckland,
g = 9.80ms−2 .
The value of g can be estimated in several simple ways, including freefall experiments (https://www.youtube.com/watch?v=uIUtf5ewhOw) pendulum experiments (https: //www.youtube.com/watch?v=6WeMbUfH1h8) and projectile experiments (https://www. youtube.com/watch?v=X1-obk6dWx4). (NOTE: Some of these YouTube videos include methods of estimating g. DO NOT use these methods - see below for a better approach using the quadratic linear model of Handout 4.)
Each row in GravityExpt.txt corresponds to a single trial. The variables are
• Time: Seconds after ejection of the steel ball, between 0.2 and 2.
• Height: Response variable - the height of the ball in metres.
Theory tells us that the relationship between height and time is quadratic, and that the true value of the coefficient of the quadratic term is −0.5g = −4.9.
Conduct a full analysis, and include Methods and Assumption Checks along with an Executive Summary. In particular, we are interested in addressing a few questions of interest in the Executive Summary:
• What is the estimated value of g?
• Is our estimated value of g consistent with the theoretical value of 9.80? [Hint - calculate the 95% confidence for g.]
• Theory also tells us that the true value of the coefficient of the intercept term is zero. Is this consistent with our analysis?
• [Optional] Refit the model without the intercept, and compare the CI for g with the CI you calculated earlier.
