Question: Galileo's experiment Galileo studied motion by rolling balls down ramps. He rolled a ball down a ramp with a horizontal shelf at the end of it so that the ball was moving horizontally when it started to fall off the shelf. The top of the ramp was placed at different heights above the floor (that is, the length of the ramp varied), and Galileo measured the horizontal distance the ball traveled before it hit the floor. Here are Galileo's data. (We won't try to describe the obsolete seventeenth-century units Galileo used to measure distance and height.)
Height Distance
1000 1500
828 1340
800 1328
600 1172
300 800
(a) Make an appropriate scatterplot for predicting horizontal distance traveled from ramp height. Describe what you see.
(b) Use transformations to linearize the relationship. Does the relationship between distance and height seem to follow an exponential model or a power model? Justify your answer.
(c) Perform least-squares regression on the transformed data. Give the equation of your regression line. Define any variables you use.
(d) Use your model from part (c) to predict the horizontal distance a ball would travel if the ramp height was 700. Show your work.