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

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.

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…