Rocket Lab

 

Equations You will want to have:

Vertical Displacement:

Y = Voyt - 1/2gt2  (Realize this is a quadratic and you will have two different times when you solve for it.  The lower time will be the Y point on the UP part of the parabola, the higher time will be the Y point on the DOWN part of the parabola.  Also realize that since I used a MINUS sign in the equation, that g = +9.8m/s2)

 

Vertical Velocity:

Vy = Voy – gt   (where t = the time UP – or DOWN – only.  NOT THE TOTAL TIME OF FLIGHT).  This is a good equation to help you determine the time it takes to get to the top of the arc since Vy at that point will be 0 m/s

 

V2 = Vo2 – 2gy (helpful for finding maximum height (y) where V = 0 m/s)

 

Range (in the horizontal (x)) direction:  Remember, this equation only works if the take off altitude is equal to the landing altitude – as it is in this lab.

Rx = (Vo2 Sin2q )/g

 

 

Procedure:

  1. Launch rocket at an angle (anything BUT 45o).  And be sure that it isn’t going to hit anything when it comes down.

 

  1. Record the q, x (distance downrange in meters) and the ttotalexperimental (Time from liftoff to touchdown.  Remember that tup and tdown are equal to ½ ttotalexperimental)

 

  1. Repeat the experiment at least three more times with the same launch angle and record your data for q, x and ttotalexperimental in a table on EXCEL.  You can find averages using EXCEL!  COOL! YOU CREATE THE DATA TABLE FOR YOUR WRITE UP.  BE SURE TO INCLUDE THE AVERAGES OF EACH OF THE DATA POINTS.  YOU’LL NEED IT FOR THE QUESTIONS. 

 

Questions:  (these are written in the order in which you should do them.  Sometimes you need the answer from one to solve later ones)

  1. Determine Vo of the rocket based on the average qexperiment you measured and the average Rangex you measured
  1. Determine Vox based on resolving the vectors from question #1 (easy!)
  1. Determine Voy based on resolving the vectors from question #1 (easy!)
  1. Use the Voy you determined in question #3 to determine the maximum height (y) reached by your rocket in flight.
  1. Predict the maximum range (in the x direction in meters) of your rocket based on the Vo you determined in question #1.  (This is why I didn’t want you to launch the rocket at 45o, since that is obviously the maximum range.  Once you predict this, we will go out and try it!)
6.       Predict the maximum height of the rocket if you were to shoot it straight up at Vo (Realize that if you shoot the thing      straight up in the air, Vo = Voy because the entire magnitude of the velocity is in the y direction.  HINT:  What will be the velocity in the y direction at the top of its flight?

NOTE:  For questions 7-10, you need to understand the following idea:  When we were outside launching rockets, we took three types of measurements:  Time, Distance (horizontal) and angle of launch.  In reality, all you need is any of the two of those to figure out the other one.  Therefore, what we are going to do in questions 7-10 is ASSUME we didn't take one of those measurements and then figure it out by calculating it.  Then we will find the percentage error between our calculated value and the one we measured in the experiment.  

  1. Use the voy you calculated in #3 to determine ttotalcalculated (we will assume for the sake of this question that you didn’t take a ttotalexperiment measurement.) HINT:  y = 0 at two points along the flight path:  at lift-off and at splash-down.  You need to find the second time (sounds like a quadratic to me)
  1. Find the percentage error between the ttotalcalculated you found in question #7 and the AVERAGE experimental value for ttotalexperiment.

% error =( ½calculated value – experimental value½/calculated value) x 100

  1. Use the AVERAGE of your experimental values for xexperiment and ttotalexperiment to determine qcalculated (we will assume for the sake of this question that you didn’t take a q measurement.  See how this is similar to question #7?  In that case we assumed you didn't take a time value.  In this case, we assume you didn't measure a qexperiment)     (HINT:  You cannot use Voy as you resolved it in question #1 because you used qexperimental to find that value.  What that means is the Rx formula cannot be used since it assumes you know Voy and q.   So, you will have to find Voy using an equation that lets you use what you know (you know  ttotalexperiment and g).  You will also have to find Vox using only xexperiment and ttotalexperiment )
  1. Find the percentage error between qcalculated and qexperimental.
  1. Assume you launch your rocket from a 100 m cliff overlooking the ocean.  Using the Vo you determined in question #1, what would its range be (in the x direction) if you launched it at a 45o angle.  Hint:   set y = -100m since it is going BELOW the horizon of launch.  Also, realize that velocity in the x direction never changes and the rocket remains in the air only due to the y component of velocity as it relates to the gravitational attraction of the Earth)
  1. Assume the same launching scenario as question #11.  With what velocity would the rocket strike the water?  (Remember that the rocket will strike the water with both a Vx and a Vy, NOT just a Vy!) Also determine the angle q at which the rocket hits the water with respect to the horizon - horizon being parallel to the water line.  

13.    Which would make the rocket go further in the x direction:  Launching it at a 45o angle (as you did in question #11)  or launching it horizontally off of the cliff (at an angle of 0o)?  SHOW YOUR WORK!  DRAW A PICTURE!       HINT:       Look at p. 157 of your textbook.

14.  Where would the paths of the rockets intersect?  For example, if you launched one at 45o and one at 0o, where would their paths cross?   a)  before they drop below the launch horizon   or  b)  after they drop below the launch horizon.  HINT:       Look at p. 157 of your textbook. And think about throwing a rock at a 45o vs. a 0o angle on a level field.

15.  Which rocket is in the air longer (time wise) the 45o launch or the 0o launch (realize they are launched with the same Vo)

 

Graphing Section:

 

1.     Assume you are going to shoot the rocket at the Vo you determined in question #1 (of the questions section) at the following angles:  0o, 10o, 20o, 30o, 40o, 45o, 50o, 60o, 70o, 80o and 90o.  Determine the Range (x) for each of these values of q.  Use GA and make one column called q.  Then, make a calculated column so that you can just enter the angle q and get the Rangex as your result. You must tell GA that you are using DEGREES and not RADIANS!  If you don’t know how to do this, look at my on-line tutorial for GA.

  Once you have calculated it,  make a Graph of  Range vs. Angle.  Angle will be your independent variable – so it goes on the x-axis.  Range will be your dependent variable, so it goes on the y-axis.  USE GA!  

When you are done, make sure you write the formula you used for the calculated column in the "notes" section of the GA - or if you are embedding your GA in an MS Word document, write the formula near the graph.  When I say write the formula, I mean write it EXACTLY as you wrote it in the calculated column, don't give me the formula as it is written in the book.  Example:  if the formula called for you to double the x and square it, you would write:  (2*"x")^2.  Notice the quotation marks around the x.  Whenever you do some mathematical calculation to a column, that column is in quotation marks.   (What I am trying to get at here is to see if indeed you know how to use GA to make a calculated column of numbers or if you are just plugging the angles into your calculator and working out the distances by hand.  Shame on you if that is what you are doing!  GA is such a wonderful tool!)

What is due for this lab?:

In this order please!

1.  Excel data table with average calculated (if I gave you the average data, you don't need to do this part).  Notice that you need to include q, x and ttotal in your table. (see PROCEDURE 3)

2.  Answer questions 1-15 and show your work!!!!!!!!!!!!!!!

3.  GA for Graphing section.  What I want to see is a calculated column on one side and the graph on the other.  Be sure to title your graph and its axis’.  Also, make sure you type out the exact formula you used to make your calculated column in GA.

 

How will it be graded?

15 points neatness

60 points #1-15 questions.  When you answer the questions, there is no need to write them out.  BUT  you must start off by writing the formula you are going to use (example:  V2 = Vo2 + 2gy) and then show me your calculations.  DON'T Just start writing numbers down!  I want to see formulas!  (Each question is worth 4 points)

25 points GA and Excel (if Excel is needed) .  Don't forget to show me your exact formula for the calculated column in GA.  If you use Excel, show me the formula you used to find averages!