Part 1:  A spreadsheet exercise

#### Problem:

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.

 v0 (m/s) Angle (deg) t (s) x (m) y(m)

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.

(Hint!)

For your laboratory report:

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

Part 2:  Projectile motion

Projectile motion is motion in two dimensions with constant acceleration.   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.

## Begin

 "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.

For your laboratory report:

 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 "Linear" and "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 click "Display equation on chart".  An equation of the form y = b1x2 + b2 x + b3 will be displayed where b1, b2, and b3 are numbers.  What do the coefficients b1 and b2 tell you? We can view the motion of a projectile as a superposition of two independent motions.  Describe those two motions.

Open Microsoft Word and prepare a report using the template shown below.

#### Laboratory 3 Report

 In a few sentences summarize the activities.  For part 2, which video clip did you choose? Insert your answers for part 1. For part 2, paste your graphs with trendlines into your document. Address the points highlighted in blue above.  Answer all questions.

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