##
* *Reflection: Real World Applications
Projectile Prediction! - Section 3: Students Prepare Their Predictions

After you teach high school physics for a few weeks, it is clear that most students hate to solve equations without numbers. They want to plug in numbers as soon as possible and this is understandable as numbers are more concrete than a letter that could be anything. However, there is value in having students derive equations without putting in the numbers right away. It is good mathematical practice and it also gives allows us to understand the relationship between variables after the derivation is done (linear, inverse, squared, etc). I tell my students this is more valuable than coming up with a single number one time. We want to know how nature operates, that if we change x, what will happen to y!

As can be seen on the first student solutions, they still struggle with this concept of formula derivation. It takes practice and perseverance and you can see that this group had to make several changes. But they can do it. The second sample shows a very neat and elegant solution. I am sure to share such a solution with the rest of the class.

In the future, I will add a challenge where students can take advantage of their derived formula. Perhaps imagine a situation where the launch velocity was changed and they must redo their calculations in 30 seconds to reposition their catch point.

# Projectile Prediction!

Lesson 4 of 16

## Objective: Given a projectile launched with a known starting velocity and angle, students will predict the horizontal position of a bucket to catch it.

## Big Idea: For a projectile where air resistance can be ignored, its horizontal velocity is constant and its vertical velocity changes at 9.81 m/s^2

*45 minutes*

In the previous lesson, Practicing Projectile Path Math, students learned how to calculate various aspects (horizontal displacement, time-of-flight) of a projectile's motion. Since I believe that *to know physics is to do physics*, students must witness that these formulas and calculations can be used to predict the landing spot of an actual projectile.

Students make calculations on where they need to place a bucket that catches a projectile that is launched with a known initial velocity and angle. If students catch the projectile in a bucket on the first launch, they receive an A+ for the activity. It is a high-stakes activity that the students find exciting.

For this problem, students use HS-ETS1-2, where they break down the problem into smaller pieces. Students will be using mathematics as applied to science and engineering solutions which is an application of NGSS Science Practice 5 as well as CCSS Math Practice 1: Make sense of problems and persevere in solving them and Math Practice 4: Model with mathematics. This is in the context of Newton's 2nd Law so NGSS HS-PS2-1 is also a part of the activity.

Supplies I have available for this activity are a Pasco Projectile Launcher, a metal bucket (the clang it makes when the projectile lands in it is a good effect!), a plastic ball to go into the launcher and a 5-meter measuring tape. I also have two clamps, for the purpose of fixing the launcher to the cart. This makes loading and firing the launcher easier and more consistent.

#### Resources

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To kick off the projectile challenge, I start off by reading this excerpt from Wikipedia and display the Projectile Challenge Power Point on the projector a picture of a human cannon ball being launched.

*The current world record for the longest human cannonball flight is 193 ft 8.8 in (59.05 m), by David Smith Jr., in Milan, Italy, 2011. The distance was measured from the mouth of the cannon to the furthest point reached on the net. David Smith Jr. was launched by an 8m (26' 3") long cannon. It was estimated that he travelled at a speed of 120 km/h (74.6 mph), reaching a maximum altitude of 23m (75' 6").*

In a dramatic voice, I tell students that today lives are at stake as they plan such an event! I give them the launch velocity and the launch angle, and working in groups of 3, their goal is to determine where to place the bucket so that they catch the projectile. All groups have the same launch velocity of 6.65 m/s, but each group has a different launch angle. This helps to prevent cheating, as each group has a different angle and thus have a different horizontal displacement.

I inform the students that before they are allowed to launch, they must complete the handout Projectile Launch Challenge. They must also devise their own scenario where some projectile is being launched and why it is critical that they must catch it on the first try.

*expand content*

To be successful in this activity, students are required to use the projectile motion equations. With the initial velocity and launch angle, students use vy = voy + gt to calculate the time-of-flight of the projectile. Once they have the time of flight, x=vxt informs them of the correct horizontal displacement. They must also draw the situation and the vectors and components as multiple representations it beneficial for student's learning.

While students work on this activity, I circulate the room to help the groups. I also assign the different launch angles to all groups, ranging from 35 degrees to a maximum of 70 degrees (anything higher and the projectile hits the ceiling). Different launch angles for each group assures that groups do not copy calculations.

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#### Time to Launch

*20 min*

Once the first group is ready to launch, I spend the rest of the class period by the launcher and don a pair of safety goggles. For each group, I check to make sure their report has all of the required elements. If it does, I give each student a pair of safety goggles. While two students measure the distance and place the bucket, I instruct the third student on how to load and fire the launcher. I like to give them as much ownership of the process as possible.

Once the projectile is ready to be launched and the bucket is in place, I interrupt the entire class for the count down. This helps to minimize unaware students from walking through the launch path. Also, this raises the excitement level as over 24 voices count down 3-2-1-FIRE! If the projectile misses to the left or to the right, I let the group try again as the launcher can be hard to line up correctly side-to-side. However, if the shot it in line with the target, this is their **one and only shot**. The reason for this is because I want to make this a high-stakes event. Groups should attempt a launch when they are confident that they have solved the problem correctly.

Based on the results of the launch, I immediately record the grade on the report. If they miss, I check my launcher values chart to see if it is a calculation mistake. If it is, I ask them to try to figure out their mistake. If they hit the bucket, I congratulate them, and give them Field Goal! to work on while the rest of the class continues to work. This is a way to differentiate since the groups who are more comfortable with the math tend to launch early. These are also groups who are more successful in completing these advanced problems; this gives them something to do while all the other groups do their launches.

In previous lessons, such as Practicing Projectile Path Math, students applied theoretic solutions to a problem. I inform students as they leave that, "TODAY, THEY HAVE DONE PHYSICS". They were given a critical problem and not only did they solve it on paper, they also made the catch in real-life.

*expand content*

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- LESSON 1: Analyzing Forces in Two Dimensions
- LESSON 2: Exploring Projectile Motion
- LESSON 3: Practicing Projectile Path Math
- LESSON 4: Projectile Prediction!
- LESSON 5: Special Case of the Horizontal Launch
- LESSON 6: Playing "A-Round" with Circular Motion
- LESSON 7: Can You Make The Turn?
- LESSON 8: Design Your Rotating Space Ship
- LESSON 9: The Pringle Package Project - Day 1
- LESSON 10: The Pringle Package Project - Day 2
- LESSON 11: Exploring Orbits Where the Centripetal Force is Gravity
- LESSON 12: The First Universal Law: Gravity
- LESSON 13: Going Full Circle on Gravity and Orbits - Day 1
- LESSON 14: Going Full Circle on Gravity and Orbits - Day 2
- LESSON 15: Accurate Model of The Solar System
- LESSON 16: Extrasolar Planets: Finding What We Can't See