This project involves an investigation of the relationship between altitude, velocity, and acceleration of the Falcon 9 Rocket. Using velocity data for a Falcon 9 flight and notions of the derivative, Riemann sum, and integral you will make predictions about the rocket’s altitude and acceleration. Each group should email me a project report that contains your figures and responses to the questions. The report must be a PDF file whose filename contains both your group number and project number. It is due before midnight on December 15, 2019.

The data for the project is attached as an excel file.

1. Create a scatter plot using the velocity data with ’time’ on the x-axis and ’velocity’ on the y-axis.

2. Using only the data, compute the acceleration at each time and create a second scatter plot with ’time’ on the x-axis and ’acceleration’ on the y-axis.

3. Using Riemann sums, determine the altitude at each time and create a third scatter plot with ’time’ on the x-axis and ’altitude’ on the y-axis. You should do this using left endpoint, right endpoints, and center points.

4. Now determine a function that models the velocity data well. Create a new figure that shows the velocity data as well as this function. Be sure to find the equation of the model function.

5. Using the model function, find both the altitude and acceleration curves. Create two new figures (one for altitude, and one for acceleration) in which the curves are overlaid with the data found above.

6. Discuss your results. Compare the various predictions and comment on why the results are similar/different.