**Exercise**

The New York Giants are tied with the Chicago Bears with only a few seconds left in the game. The Giants have the football and call the place kicker into the game. He must kick the ball 52 yards (47.5 m) for a field goal.

If the crossbar of the goal is 10 ft (3.05 m) high, and the maximum speed with which the kicker can kick the ball is 25 m/s, which range of angles (in deg) will allow him to score the field goal?

Solve this problem using a spreadsheet. Produce a spreadsheet with 5 columns.

v_{0} (m/s) |
Angle (deg) | t (s) | x (m) | y(m) |

Hint: Download this spreadsheet to get started.

The first two columns each contain one entry each. Construct your spreadsheet so that when you change these numbers, the numbers in the next three columns will be updated. The time steps in the t(s) column should be on the order of 0.1 s or smaller. The entries in the x(m) and y(m) columns are calculated as a function of time using the kinematic equations.

In one full sentence answer the question posed in the problem.

**Experiment**

Projectile motion is motion in two dimensions under the influence of a constant force.
It is hard to get detailed information about its motion without using external
measuring instruments. In this experiment the instrument is a video
camera. You will analyze a video clip. The clip shows a person
throwing a ball. You will determine the position of the ball in two
dimensions as a function of time by stepping through the video clip
frame-by-frame and by reading the time and the position coordinates of the ball
off each frame. You will construct a spreadsheet with columns for time and
position and use this spreadsheet to find the x and y component of the velocity
as a function of time.

Procedure:

To play the video clip or to step through it frame-by-frame click the "Begin"
button. The "Video Analysis" web page will open. Choose one of the throw_x.avi video
clips.

- "Play" the video clip. When finished, "Step up" to frame 0
- In the setup window choose to track both coordinate of the object.
- Click "Calibrate". Click "Calibrate X". Calibrate the x-axis as in lab 1. Then click "Calibrate Y". Calibrate the y-axis as in lab 2.
- Click the button "Click when done calibrating". A spreadsheet will open up. Click "Start taking data".
- Start tracking the ball. Position the cursor over the ball. When you click the left mouse button, the time and the x- and y-coordinates of the ball will be entered into the spreadsheet. You will automatically step to the next frame of the video clip. When done, click "Stop Taking Data".
- Your table will have 3 columns, time (s), x( m), and y (m).
- Open Microsoft Excel, and paste the table into an Excel spreadsheet.

Produce graphs of the x and y components of **position versus time**.
Label the axes.

- Describe the graphs? Does one of the graphs resemble a straight line? If yes, what does this tell you?
- Right-click your data in the x(m) versus time graph and choose "Add Trendline". Choose "Type, Linear" and "Options, Display equation on chart". An equation y = ax + b will appear on your graph, where the number a is the slope and the number b is the y-intercept. What is the physical meaning of the slope of this graph?
- Right-click the data in your y(m) versus time graph and choose "Add
Trendline". Choose Polynomial, Order 2 and under options click "Display equation on
chart". An equation of the form y = b
_{1}x^{2}+ b_{2}x + b_{3}will be displayed where b_{1}, b_{2}, and b_{3}are numbers. What do the coefficients b_{1}and b_{2}tell you? - We can view the motion of a projectile as a superposition of two independent motions. Describe those two motions.

Paste your graphs with trendlines into your log.

Convert your log into a lab report.

**Name:E-mail address:**

**Laboratory 3 Report**

- In one or two sentences state the goal of this lab.
- Insert your log with the requested graphs and the answers to the questions in blue font.

Save your Word document (your name_lab3.docx), go to Canvas, Assignments, Lab 3, and submit your document.