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=Week 4 - Putting it all together - The Grand Projectile Challenge!=

**1) Introduction**
** Over the last couple of sessions, we have looked at the world through the eyes of one and two-dimensional projectiles. We have analyzed objects dropped from high above and shot over vast distances. We have even used our projectile intuition to battle each other in gladiatorial combat. Since, "there can only be one", the winner of last session's tournament is: [insert winner]. Congratulations!

[ insert live tournament bracket ] ** [ insert live tournament bracket ]


 * For this session, we will once again return to the tournament environment. Instead of relying on the "good enough" level of accuracy that we did on our computerized battlefield, we are going to aim for more precision and control of our projectiles by ** adding mathematical substance to our growing intuition . As the famous saying goes, " ** Almost only counts in horseshoes and hand grenades"... and tanks.

We will once again use our equations of motion to hit various ground targets, but this time with greater accuracy. If need be, you can even perform calculations by hand as there is a one-to-one match between challenge results and the math needed to attain them. To complicate matters even further, we will step outside of the idealized models that we have been using and begin to incorporate real-world external influences such as drag and wind currents into our calculations. **

**2) Review**
Last session, we saw come out victorious. They were able to demonstrate the necessary projectile intuition to estimate launch angles and velocities for covering various ranges and altitudes.


 * //Review Question 4.x//** //- Why do you think this person won? What strategies did you use to hit your target? For example, what corrective actions did you take when you overshot your target?//


 * //Thought Question 4.x//** //- Do computer games use the same equations of motions that we use in this course? Why?//

We also worked on establishing our own company, //Projectile Messaging,// to compete head-to-head with the Postal Service//.// We completed a launch flight log for message canisters bound for an assortment of locations.

We saw some pretty ones ranging from _ and _ to __and__ _.

The max distance award goes to co-founder [insert name] with a range of [insert value]. The maximum height award goes to to co-founder [insert name] with a height of [insert value]. The maximum air time award goes to to co-founder [insert name] with a time of [insert value]. The express mail minimum time award goes to to co-founder [insert name] with a time of [insert value].


 * //Thought Question 4.x//** //- How would these values change if we used a more massive canister - 10Kg instead of 5Kg?//
 * //Thought Question 4.x//** //- How would your approach to the problem change if we added 1Kg to the canister at each location?//
 * //Review Question 4.x//** //- This game was fun, but how would you improve it to make it more fun? To make it more realistic?//

We also learned that we can decompose vectors into horizontal and vertical perpendicular ** components and treat them independently. This allows us to solve harder higher dimensional problems by breaking them down into much simpler one-dimensional ones.

//Thought Questions 4.x//** //- Can you visualize vector diagrams of your projectiles at various points in flight? What do the horizontal and vertical components look like in your own words? Do they change through out the flight? If so, how?//

//**Thought Questions 4.x -** If a Projectile Messaging client asked us be extra delicate with the contents of their canister and minimize vertical impact, how would we go about accommodating them?//

**3) New Content and Assignment**
Many introductory science courses make content concessions to smooth the learning process. In physics for example, we often defer resistive influences such as friction, drag, and wind effects until basic concepts have been mastered. Because all of these influences can have vectorial impact, we also benefit from the fact that they can be easily added on later using the tools and techniques that we have already developed. For example, adding wind effects to our previous projectile problems would only require us to add in an additional velocity vector representing the wind. Once we have the vector sum, the problem can be solved exactly the same way that we have been solving other projectile problems.

Here is a passage from a ballistics publication talking about the impact of wind resistance. Try to visualize what they are saying in physics terms.

//**5.3**// **//Wind Effects//** //A bullet's reaction to a wind depends very much on both the speed of the wind and the direction in which it blows. In the first place, a headwind or a tailwind causes a vertical deflection (a change in drop) of the bullet, while a crosswind causes a horizontal deflection. It also happens that a crosswind causes a much larger deflection than does a headwind or tailwind of the same speed. As an example, take the .308 Winchester cartridge loaded with the Sierra 190 grain HPBT MatchKing bullet at a muzzle velocity of 2500 fps. At a range of 600 yards, a 5 mph headwind would cause the bullet to strike the target 0.30 inch lower than it would with no wind. A 5 mph tailwind would cause the bullet to shoot high by the same amount. In either case, a well-aimed shot certainly would stay within the X-ring on the 600 yard target. But a 5 mph crosswind would deflect the bullet 14.35 inches to one side, with a devastating effect on the shooter's score if he hadn't made a windage correction.//

//This example is very typical of the relative importance of a crosswind as opposed to a headwind or tailwind. As we will show a little later, the effects of a headwind or tailwind can be neglected for almost all shooting situations, except perhaps for extra long range (1000 yard) target shooting in strong winds. Crosswinds, though, are important for hunting as well as target shooting. The crosswind deflections in the Ballistics Tables show how much crosswinds affect each Sierra bullet, and it is clear that both hunters and target shooters need to be aware of the importance of crosswinds.//

**//**Thought Question 4.x** -// //What units of measurement are being used in the passage? Are they consistent?// The impact of air resistance http://www.physicsclassroom.com/mmedia/newtlaws/efar.cfm http://www.physicsclassroom.com/mmedia/newtlaws/sd.cfm http://www.physicsclassroom.com/class/newtlaws/U2l3e.cfm
 * //Thought Question 4.x -//** //What is another way of phrasing what a bullet reacts to?//
 * //Thought Question 4.x -//** //Can you take these prose and visualize what they are saying with the information we have learned this unit?//
 * //Thought Question 4.x -// //Why might crosswinds have a greater impact on a projectiles than head or tail winds?//
 * Thought Question 4.x** - What does this mean for our canisters at //Projectile Messaging//?
 * Thought Question 4.x** - How are wind effects and air resistance different?

Experiment with the projectile simulator again. This time, click on the "air resistance" checkbox.
 * Interactive Examples**

Notice how different the trajectories are when we go from an ideal "lab" simulation to a more real-world one.
 * //Review Question 4.x -//** //From the graphic above, do you think the pink projectile's smaller parabola is the result of air resistance or wind effects? Why?//

//**
 * //Teacher Crafted Activity 4.x : Inserted Dynamically by Teacher Assignment Administration Page

**4) Assignment Submission**
Now that we have come to the end of the unit, it is time for the GRAND PROJECTILE CHALLENGE! Challenge... challenge... challenge...

This Grand Challenge will draw on all of the knowledge that we have been exposed to over the last four sessions.

You will be required to:
 * 1) Solve 10 interactive projectile problems similar to the ones that we have previously seen.
 * 2) Answer 5 short answer questions on vectors, equations of motion, and one and two-dimensional projectiles.
 * 3) Answer 5 more interactive projectile problems, but this time from a pool of challenges created by your groupmates!

That's right, you will be required to both solve AND create projectile problems. Challenges sourced from your classmates will be grouped into pools from which 5 will be assigned at random. If two problems are the same, you will walk the list of questions from the first duplicate until you find a problem that is unique to you.

We will be using a simulation from the University of Colorado to score our challenges. If you successfully hit the target, it will let you know - Score!



You will need to:
 * 1) Create a google spreadsheet file to hold and format your answers. You can "make a copy" of this template
 * 2) Add a good challenge question for each student in your group to your group's question page . Be creative, by mixing known and unknown parameters and choosing different types of objects that you want your group mates to launch. Remember to place one challenge per line and label each one from 1 through the number of people in your group. Illogical problems will be flagged and reported, so test them out and make sure they make sense //before// making them public.
 * 3) You can find your random set of 5 challenge problems [ here ]. [ write quick code for a "choose 5" algo ]

Once you have completed your challenge answer sheet and are ready to submit, please send a link to your answer sheet via Edmodo by noon on XYZ.

// Your unit score will be a function of how well you hit both student and course configured challenge targets, how accurate your short answers are, and the quality of your challenge submissions - do your problems make sense? //

Here is a check list for what you have to complete for the challenge:
 * 1) [ - ] Solve 10 course-created projectile problems.
 * 2) [ - ] Answer 5 course-created short answer questions.
 * 3) [ - ] Create unique challenges for each of your group mates. * You may not  repeat challenges within your group.
 * 4) [ - ] Solve 5 randomly selected problems from your group question pool.
 * 5) [ - ] Have fun!

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 * Take a Quiz and see what you know**

Please remember to review and vote on the best student questions from the previous session for inclusion in our year end course guide. The questions are maintained by UserVoice. See sample below.
 * Vote, rank, and discuss them each week! **



**5) Personal Learning Log Contributions**
** As we do at the end of each session, we will contribute a summary of what we have learned in our own words, images, and links to our personal course review log. The purpose of which is to evolve a review book for the entire course.

Additionally, each of you will submit three unique questions and answers based on the content learned this session. Make them fun and challenging for your classmates. We will vote on the best ones, so be creative!

As we do at the end of each unit, we will also create an end of unit review outlining important points and formulas from the entire Projectile unit.

An example of an important point might be: ** //Free falling objects in a vacuum accelerate at the same rate (a=g=9.8m/s²) regardless of mass. An example of an important formula might be: // math s_i=s_0+v_0t+.5at^2 math

//current position = initial position + initial velocity x time + 1/2 current acceleration x time squared//