Launch Angle, Velocity, Range, and Height

In my Principles of Technology class, we are preparing for a water balloon launching project. Teams have to build a rig to launch a water balloon at a target.

The targets are placed at fixed intervals of 20 yards, 40 yards, and 50 yards from the launchers. At each target site will be either a school administrator or myself.

Before launching, each team must present their mathematical proofs of concept of how they ensure they hit their target(s).

Leading up to several days of building, we are taking a test over these calculations.

Launch Angle Calculator

Launch Angle Exam Review Guide

Launch Angle Exam Review Guide Answers

As several of my students have not yet covered Trigonometric mathematics, I have provided a quick “plug-and-chug” worksheet in Excel that solves for the missing equations.

It will solve for the following:

  • H when given Vo and Theta
    • =((((B2)^2)*((SIN(B4))^2)))/(2*B5)
  • R when given Vo and Theta
    • =((((C2)^2)*((SIN(2*C4)))))/(B5)
  • Vo when given H and Theta
    • =SQRT((D6*(2*D5))/((SIN(D4))^2))
  • Vo when given R and Theta
    • =SQRT((E7*E5)/(SIN(2*E4)))
  • Theta when given Vo and H
    • =ASIN(SQRT((F6*(2*F5))/((F2)^2)))
  • Theta when given Vo and R
    • =ASIN((G7*G5)/((G2)^2))/2

Projectile Motion Worksheet #2

My Principles of Technology class is continuing to work on the preparations for the projectile motion project of launching a water balloon at me from 40 yards away.

Today, we analyzed how to calculate the maximum height and maximum range of a projectile.

I first showed them the formulas and we pulled apart the variables:

Maximum Height and Range Formulas
Maximum Height and Range Formulas

We then discussed that the mass of the object does appear as any of the variables. We discussed why this is and then watched the following video:

Afterward, we started to work on the problems in the following online worksheet.

Projectile Motion Worksheet

The first 5 questions are short answer and will vary by student. The answers to the last 15 questions are provided at the link below:

Projectile Motion Worksheet Solutions

Up next, we will analyze drag coefficients and the impact of air/wind resistance on the flight path of the balloon.

We’ll then move into designing a launch apparatus that can launch the projectile at the correct angle and velocity.

Finally, we’ll move to testing. Fortunately, for this project, no fires!

 

Projectile Motion Worksheet #1

In my Principles of Technology class, we are starting to gear-up for a projectile motion project. The students will be working in teams and launching a water balloon at me from exactly 40 yards away.

In the first worksheet in the series, students were given a series of right triangles with sides A and B given. Sometimes the units were the same and other times they would have to convert units.

ABCx Triangle
ABCx Triangle

The students were asked to calculate the length of C in the most appropriate units and then calculate angle X using the trig function (sine, cosine, or tangent) of their choice.

All of my students were able to perform the first calculation using the Pythagorean Theorem. The second calculation, even through it was given step-by-step, was not completed by the majority of the students who are in Algebra I.

The claim was that they had never seen it before. Obviously, I countered with, “Well, you have now.”.

QR Electromagnetism

Upon returning from Thanksgiving Break, we’ll be starting a study of electromagnetism in my Principles of Technology class. To start with, we’ll be doing a QR Knowledge Hunt.

Electromagnetism Knowledge Hunt Cards

The 15 cards are placed on the walls around random parts of the main hallway. The class is broken into 12 teams of 2 and each team is assigned a starting number. Teams must move through all 15 cards in any order they would like as long as there is no unnecessary “congregating” around any single card.

Electromagnetism Knowledge Hunt Card #1
Electromagnetism Knowledge Hunt Card #1

This particular knowledge hunt requires the students to utilize a QR scanner to “read” the question.

They must scan the QR code and then either use their existing knowledge or research skills to answer the question. The answers are then recorded on a provided answer document, which is submitted for a grade from each team. Only one answer document is needed from each team as long as both team members names are on the answer document.

Here are the questions they are having to answer (in no particular order):

  1. In electromagnetism, electric current is measured using which SI unit?
  2. In electromagnetism, what does the SI unit of a coulomb measure?
  3. In electromagnetism, what does the SI unit of a farad measure?
  4. In electromagnetism, what does the SI unit of a tesla measure?
  5. In electromagnetism, what does the SI unit of a volt measure?
  6. In electromagnetism, what does the SI unit of a watt measure?
  7. In electromagnetism, what does the SI unit of an ohm measure?
  8. Nikola Tesla is best known for his work on what?
  9. The electromagnetic force is one of the 4 forces of nature.
  10. What are the names of the poles of a magnet?
  11. What electrical charge discovery is Thomas Edison credited with that was the “opposite” of the work of Nikola Tesla?
  12. What happens when identical poles of a magnet are placed near each other?
  13. What happens when opposite poles of a magnet are placed near each other?
  14. Who is credited with the discovery of induction (production of an electromotive force (ie voltage) as a result of the interaction between two magnetic fields)?
  15. Who is the French mathematician and physicist, considered to be the father of electrodynamics?

Following the delivery of the exercise, I will be posting an answer key to this exercise.

Trebuchet Assault

Recently, in Principles of Technology we wrapped-up motion and acceleration with a project involving construction of a small-scale trebuchet made of popsicle sticks, rubber bands, and any other materials that could be secured to defend an assigned army.

Soldiers Guarding the Trebuchet
Soldiers Guarding the Trebuchet

We competed in a bracket elimination system. Each team started with their trebuchet and 20 soldiers. Each team took one turn shooting at the other. Any soldiers who are hit were removed from play.

At least 2 soldiers were required to be standing to fire the trebuchet. Students asked during the competition if they could use their “dead” soldiers as ammunition. I agreed and it turned out to be surprisingly effective.

If the trebuchet itself was hit, it was unable to return fire for one round to undergo “repairs”. At least 5 soldiers were required to complete repairs to the trebuchet.

If a team dropped below the minimum number of required soldiers for their next move, they were eliminated.

The students found the entire game very interesting and understood the physics behind all of it.

For a final battle, we broke everyone into 2 large groups and fought against each other in a rapid open-fire exercise.

Eggs Away! Look Out Below!

Egg Drop Experiment
Egg Drop Experiment

In my Principles of Technology class, we performed the classic “egg drop” rig building experiment. As this is a fundamental physics class, we’re using this to discuss Unit 2: Conservation of Energy and Momentum where we cover Newton’s 3 laws of motion.

The students were given three 90-minute class sessions to research ideas for their drop rigs and to build them.

Following these three class sessions, we performed the drops.

The first drop was done from the ground at a height of 2 meters (~6.56 feet). Of the 20 rigs that were dropped, 18 survived and 2 failed.

The second drop was done from the basket of a pneumatic boom lift at a height of 7 meters (~22.96 feet). Of the 18 rigs that were dropped, 10 survived and 8 failed.

The third drop was also done from the basket on the boom.lift at a height of 15.5 meters (~50.85 feet). Of the 10 rigs that were dropped, 5 survived and 5 failed.

The final drop was done like the third drop, but each rig was thrown as opposed to only being accelerated by gravity. Of the 5 rigs that were thrown, 3 survived and were declared the “winner” and 2 failed.

Panoramic Image from Lift of FHS
Panoramic Image from Lift of FHS

Following the last drop, I took a quick panoramic picture using Google Cardboard Camera. It was a nice view around Ferris today!

Air Skimmers Project

Our next unit in Principles of Technology is the building of “air skimmers” for the intoduction into our second instructional unit – Energy and Momentum.

In this unit we cover the following TEKS:

(9)  The student describes and applies the laws of the conservation of energy and momentum. The student is expected to:

(A)  describe the transformational process between work, potential energy, and kinetic energy (work-energy theorem);

(B)  use examples to analyze and calculate the relationships among work, kinetic energy, and potential energy;

(C)  describe and calculate the mechanical energy of, the power generated within, the impulse applied to, and the momentum of a physical system; and

(D)  describe and apply the laws of conservation of energy and conservation of momentum.

Here are the parts for mine cut and ready. Planning to allocate a full 90-minute class to measuring, cutting, and drawing.

We’ll do assembly for the first half of the next class and then discuss the math and science behind what is going to happen.

The following class period, we’ll launch and see who goes the farthest and fastest.

Mousetrap Racers

One of the projects that we do as part of Unit 1 – Motion in Principles of Technology is the “Mousetrap Racers”. These are the kits that come with basic materials for building a race car driven by a mousetrap. However, there are no directions.

In my case, students were working in groups of 2 and had 3 90-minute class periods to prepare their cars. They could use anything from within the classroom on their race cars.

Here are the pictures of their creations…

Water Bottle Rocketry

We started the school year in Principles of Technology with a bang – more like a blast!

The first project, right out of the gates, was soda-bottle water rockets. This was the introductory project for the course and for Unit 1 – Motion.

The class was broken into self-selected teams of 1 to 3. The class was given a complete 2-liter soda bottle and access to random materials from around the classroom. The teams were given 3 90-minute class sessions to brainstorm and complete their rocket designs.

Upon completion of the designs and following the launches, teams completed force diagrams and a post-launch analysis explaining why their rockets performed the way they did.

Here are the various rockets on the morning of the launches…