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.”.

Getting Hot in Physics

Well, to say that today did not go as expected would be the understatement of the school year!

My Principles of Technology class has been working on building model rockets as part of a unit that was analyzing the physics concepts of impulse, velocity, and acceleration, the chemistry concept of balanced chemical equations/reactions, and the engineering concept of technical drawing/documentation.

Today was the day that we launched. We had 6 small single-stage rockets to launch in addition to 2 small two-stage rockets.

Each single-stage rocket was loaded with a single A-rated motor which would carry it to a total altitude of approximately 250 feet. Each two-stage rocket was loaded with two C-rated motors which would carry it to a total altitude of approximately 1,800 feet!

Before going outside, we verified the weather conditions, which showed winds from the west at 7 MPH with guests to 11 MPH. The humidity was 41% and dropping. We decided to launch from the west side of the property with the idea that the winds would carry the rockets onto the soccer fields which had recently been watered.

Rocket Launch Site
Rocket Launch Site

Our first launch of the morning performed as expected and came down next to the roadway by the launch site.

Our second launch of the day did not perform as well. The first stage of the rocket fired as designed and carried the rocket to around 900 feet. Unfortunately, the first stage did not properly separate as designed and the rocket began to tumble back to the ground.

After a few seconds, the second stage ignited which sent the rocket flying on the path it was pointing at, which was toward the ground west of our launch location and it ignited the cardboard frame of the first stage which was now in a free-fall into the field to the west of the launch location.

Rocket Crash Site
Rocket Crash Site

The rocket came down about 100 yards west of the launch pad and the first stage landed about 30 yards to the east of the crash site. Unfortunately, since the first stage was on fire when it landed and it landed in a field of 1 meter tall grass/hay, the field was quickly engulfed in fire.

Rocket Burn Area
Rocket Burn Area

Ultimately, the crash resulted in the burning of approximately 1 acre of grassland which is fortunately owned by the school.

Because of the quick response of the Ferris Fire Department, the fire was quickly contained and everyone was safe with the only loss being the grassland, the rocket launcher, and the rocket launch stand.

Burned Field
Burned Field
Burned Launcher in Grass
Burned Launcher in Grass
Burned Launcher Inside
Burned Launcher Inside