Special Case of the Horizontal Launch
Lesson 5 of 16
Objective: Students apply projectile motion equations to the special case of a horizontally-launched projectile.
In today's lesson, students learn how to solve the much simpler problem of a horizontally launched projectile. This is a simpler situation than projectiles launched at an angle, as seen in Practicing Projectile Path Math, because it is easy to determine the time it takes a projectile to hit the ground. A horizontally launched projectile has a time-of-flight that is that same as an object that is dropped. The reason I present this concept last is because I have found in the past that many students would use the solutions for this problem to solve the more complicated problems. By presenting this situation last, I remove the distractions of this simple solution and require students to fully analyze how a projectiles velocity components change with time.
I use a device called a "Vertical Acceleration Demonstrator" produced by Arbor Scientific. This device demonstrates that a dropped ball and ball launched horizontally hit the ground at the same time.
Because of the mathematics involved in the case of the horizontal launch, CCSS Math Practice 2: Reason abstractly and quantitatively is applied along with NGSS Science Practice 5: Using mathematics and computational thinking. The content is all in the context of NGSS Performance Standard HS-PS2-1, the mathematical relationship between the net force acting on an object and its acceleration.
I open the class with a "do now" problem projected on the screen with the horizontal launch Power Point. I shows a jet that drops a bomb. I ask the students to draw the situation in their notebooks and predict the path that the bomb would follow as viewed from inside the bomber and then again, predict the path that the bomb would take as viewed from a stationary observer on the ground outside. Visualization is an important skill in physics and this activity helps students develop visualization skills. After they have made their predictions in their notebooks, I show the bomber video which gives the perspective of a bomb drop from within the bomber and one that shows a bomb dropped from the perspective of another bomber that is flying along side. This video is used to demonstrate the correct answers. The Power Point also has animations to help students with this understanding.
There are also slides in the Power Point with a gun and a bullet as a horizontally launched projectile. These slides are for later in the lesson.
I do a quick demonstration that shows how two projectiles, one dropped and one launched horizontally, hit the ground at the same time. Arbor Scientific sells this device. I first ask the students to vote, by raising their hands, which ball they think will hit the floor first, the dropped ball or the launched ball or do they hit at the same time. I do the demo and students see that they do hit at the same time.
The animated picture to the right demonstrates this concept (there are several other engaging videos on the website to which that video is linked).
Once they have seen for themselves that the projectiles time in the air is independent of the launch velocity (as long as it is launched horizontally) I finish presenting the horizontal launch Power Point. Students are to take notes in their notebooks on how to solve a the problem of the horizontal launch which is detailed step-by-step in the Power Point.
Students Practice Problems
After students have taken notes on how to solve these problems, I provide students the opportunity to practice these concepts so as to help them apply the concepts we just learned and make them a part of their problem-solving skills. I hand out the Horizontal Projectiles worksheet. Students are to work alone as these problems are relatively simple. They have 10 minutes to work on the problems. While they are working on the problems, I walk around the classroom and give support where needed. I carry the Horizontal Launch Solutions with me so that I can check their work as they do it. I expect that students complete for homework any problems they do not finish during class. In fact, most students do not finish. However, I make sure to leave 20 minutes at the end of class to show a video.
Mythbuster Test It Out!
The final 20 minutes of class I show these excellent Mythbusters videos.
In this segment, they refer to the "classic physics problem" of a bullet fired horizontally from a gun hitting the ground at the same time as a bullet that is dropped from the same height. Students eyes go wide as this video begins, because they will get to see this problem put to the test! The Mythbusters position the dropped bullet over the spot where they predict the fired bullet will hit the ground to see if the bullets will hit the ground at the same spot, at the same time.
It is not only a great science video that tests out the concept that was just presented, but the Mythbusters have to do a fair amount of engineering to get their firing rig to work right. I skip segments 2 because it is a failed attempt to test out this idea with a paint ball gun. In the interest of time, I also skip segment 3 which shows how they get the horizontal launch distance for the fired bullet.
Today students learned that a horizontally launched projectile takes the same amount of time to hit the ground as an object dropped from the same height. This is not an intuitive fact and it is a great application of the independence of the x and y components of an object in motion.