Extra Credit #1

Begins Oct 17, 2016

The purpose of this assignment is to allow students to demonstrate their understanding of various abstract and applied physics topics. Because of the nature of this assignment, it will be graded fairly strictly—pay close attention to the Notes below. Assignments which are not completed as required will not be evaluated.

NOTES:

  1. The Extra Credit Assignment consists of five problems, to be completed outside of class.
  2. This assignment is Extra Credit and not required.
  3. This assignment is intended to provide students with the opportunity to review some of the material we've covered, and not all students need the same amount of review. Students will be eligible to receive credit on problems completed according to the table below.
    Your Test Average (incl. Ch 5-6 test)Review Problems You Are Eligible to Complete
    0 - 69%Problems #1 - 5
    70 - 79%Problems #2 - 5
    80 - 89%Problems #3 - 5
    90 - 100%Problems #4 - 5
  4. The total points earned by a student on this assignment will be determined by the instructor based on a number of factors, including number of problems completed, difficulty of problem, and overall quality of assignments submitted by students.
  5. You may work on the problems with other people—in fact, this is encouraged—but each person must complete his or her own assignment to be turned in. Even when numeric answers to problems are the same, solutions from different students must be written independently, and differently, and developed and explained in each student's own words.
  6. The assignment must have a separate cover sheet that includes your Name, Date, Course and Period, and Name of Assignment. Staple this cover sheet to the front of the problems that you've solved.
  7. Each response must be hand-written on a separate piece of paper, which must include:
    a) Your name and the problem number at the top of the page.
    b) Salient details from the original question written out as appropriate.
    c) Your solution, hand-written in blue or black ink, with all work shown in detail.
    d) Drawings, diagrams, or graphs with labels must be used to explain your solution more clearly.
    e) Written explanations (blurbs, in English) explaining important steps in your solution.
    f) The final answer, with a box around it.
    See below for an example.

    If this seems like an awful lot of work, it is! Remember that this is Extra Credit: you're trying to impress the instructor with how well you can do. If in doubt, do a little more than you think you should, rather than trying to get by with less, at the risk of losing points on your solution.
  8. The assignment will be available online on Monday, Oct 17 on the Internet at http://www.crashwhite.com/apphysics/
  9. The instructor will be available to answer questions about the assignment on a limited basis: before school, after school, and possibly by e-mail. The instructor will not be able to help you if you leave all of your work until the night before the assignment is due.
  10. Your completed assignment must be turned in directly to the instructor anytime before 3:00 PM on Friday, October 28.

EXAMPLE PROBLEM AND SOLUTION:

SAMPLE PROBLEM:

In "The Matrix," Neo is given a test by Morpheus, who asks him to leap from the top of one building to another. Assume the buildings are each 100m tall, and 15m apart. Neo runs and leaps from the first building with a velocity of 5.00 m/s at an angle of 36.9 degrees (toward the second building).

a. Will he make it to the next building?
b. Where exactly will Neo land?

(Assume no air friction in this problem.)

EXTRA CREDIT PROBLEMS

1. Volleyball Serve

Watch the video of Becca Hanel serving a volleyball. Using time data taken from the video (which runs at 30 frames per second) and reasonable distance/length estimations, calculate the initial velocity of the ball as it is served.

Carefully explain and document your reasoning, in words and calculations.

2. Motorcycle's Coefficient of Friction

In the 2012 MotoGP race in Silverstone England, TV coverage provided data for some motorcycles' position on the racetrack and speed at that location (see video clip). By taking some screenshots, searching on Google Maps for the racetrack, and using Adobe Photoshop layers, I was able to do some additional graphical analysis (shown here).

Based on information gained from these preliminary analyses, determine the coefficient of static friction between the motorcycle's tires and the road.

Carefully explain and document your reasoning, in words and calculations, and comment on how reasonable you think your results are.

3. Polytechnic Drinking Fountain

a. Take a digital picture which clearly shows a drinking fountain at Polytechnic, your face, the water's full trajectory as it leaves the fountain's spout, and at least part of a vertically oriented meter stick. By printing this picture and using the meterstick as a scale, you can make various length measurements (horizontal and vertical) to help you solve the other parts of this problem. It's appropriate for you to draw on the photo any lines or guides that will indicate measurements you made using the photo.

b. calculate the x and y components of the water's velocity at the point where the water leaves the fountain.

c. calculate the amount of time it takes for the water to reach its highest point.

d. Determine the angle (relative to the horizontal) of the initial velocity at the point where the water leaves the fountain nozzle by two different methods, and calculate the percent difference between the two values.

Method 1: Measure the angle on the photograph using a protractor.

Method 2: Calculate the angle based on your answers to part b.

e. Develop an equation to describe the water's trajectory (x and y coordinates) as a function of time.

4. Driving in France

Driving along a 4-lane highway (autoroute) in France, I noticed a big sign that said "Un trait = danger - deux traits = sécurité!" I didn't know what a "trait" was, but the graphic on the sign suggested that they were the long, regularly spaced lines that lined the edge of the road. I presumed that the lines had a length that corresponded to how much distance you should leave between your own car and the car in front of you.

I noticed that the lines followed this sort of pattern:

    ************    ************    ************   
with the lines approximately three times as long as the spaces between them.

As we sped along the road, I noted that the car I was in was traveling at approximately 110 km/hr, which is the speed limit along this autoroute. I used the stopwatch on my watch to take some data on how much time passed from the start of one line to the start of the next line, and recorded the following values:

1.67s
1.85s
1.75s
1.73s
1.85s
1.73s
1.79s

Based on the information given:

a. What was the speed of the car in meters per second, and the average time from one line to the next?
b. What is the distance from the start of one line to the start of the next?
c. How long was each actual line, not including the space between one and the next?
d. How long are these lines, actually? (Research on Internet)
e. What was the percent error between my results and the real length of each line?

I also managed to record a few seconds of traveling down the road with my camera, which shoots video at 30 frames per second. When this video was made, the driver reported that the car was traveling at 113 km/hr.

f. Given the known length of the lines based on your research for (d) above and using frame counts from the video, what is the car's actual speed? What is the percent difference between this value and the 113 km/hr reported by the driver?

The French road sign says that "Two lines = security!" (On the other hand, France has one of the highest accident rates in Western Europe, although it still significantly lower than that of the U.S.)

g. Given the data collected and the analysis you've done, is it correct to say that leaving "two lines" of space between you and the car in front of you will ensure avoiding a collision with the car in front of you? Explain in a few sentences, and provide quantitative evidence in your analysis.

5. The Matrix: APUs vs. the Sentinels

Sentinels are invading Zion. One in particular is flying in a complicated pattern, its time-dependent position in three-dimensional space given by the functions

xsentinel=200t+a, where a is your birthdate (a number from 1-31) and positive x is in an easterly direction.
ysentinel= 100t+450, where positive y is in a northerly direction.
zsentinel=bt, where b is your birth month (a number from 1-12) and positive z is in the up direction.

Thus, if you were to choose a time t, these functions will tell you the x-, y-, and z- coordinates where the sentinel is located at that time.

 

The APU units, shown to the right, fire projectiles at the sentinels. Assume that Zion is located in a region where the acceleration due to gravity is the same as on Earth, and air friction is negligible. If the APU is located at the origin (0,0,0) and the projectiles are fired with an initial velocity of 300 m/s at time t=0, in which direction should the APU be aimed to hit the sentinel following the path described above? (In other words, if you fire the APU at time t=0, where should you aim the projectile so that its x-, y-, and z-coordinates will intersect with the coordinates of the sentinel?) Give your answer in horizontal degrees relative to 0 degrees east, and degrees above the horizon.