Skyward Bound Slides Skyward Bound
Mastering Maximum Height
11th Grade Physics | Kinematics
Warm-Up Challenge
5 Minutes
"Imagine a basketball free throw. You freeze-frame the ball exactly at the highest point of its arc."
The Question:
What is the vertical speed ($v_y$) right now?
FREEZE FRAME
Target
Answer: 0 m/s
Video Case Study
Physics in Action
Embedded media
Focus Areas:
1
The Dumpling Rule: Watch the peak at 2:48.
2
The 5-Step Process: Sketch to Solution.
3
Calculation: Find the firework's height.
Watch: 2:48 — 7:17
The "Stop" Point
"Before an object can fall back down, it must momentarily stop. At maximum height, vertical velocity is zero."
\[v_{y,f} = 0\]
at Max Height
Key Equation:
\[v_{y,f}^2 = v_{y,i}^2 - 2g(y_f - y_i)\]
\(v_{y,f} = 0\)
\(y_i = 0\) (launch)
\(g = 9.8 \text{ m/s}^2\)
Solve for \(y_f\)
The Water Balloon Toss
Action Lab
Set the Angle
Use the launcher to lock in your assigned angle (30°, 45°, or 60°).
Time the Flight
Start on launch. Stop the instant it hits. This is your t total.
Calculate Height
Use your flight time to calculate how high that balloon flew.
Pro-Tip
Remember: \(t_{peak} = t_{total} / 2\). Vertical is independent!
Skyward Bound Worksheet Skyward Bound: Water Balloon Lab
Projectile Motion & Maximum Height Investigation
Name:
Date:
Objective
Calculate the theoretical maximum height of a water balloon based on its total flight time and launch angle. Compare your calculation with visual estimates from your team.
Assigned Angle
30°
45°
60°
Step 1: The Flight Path
Sketch the trajectory (label peak as \(v_y = 0\))
Prediction:
Based on how hard we pull back the launcher, I expect the balloon to reach a height of approximately:
______ meters
Step 2: Launch Data
Trial # Assigned Angle (\(\theta\)) Total Flight Time (\(t_{total}\)) Visual Height Estimate (m) 1 2
Step 3: Calculating Peak Height
Pick your "best" trial and show your work below. Use \(g = 9.8 \text{ m/s}^2\).
A. Calculate time to reach maximum height (\(t_{peak}\)):
Formula: \(t_{peak} = t_{total} / 2\)
B. Calculate initial vertical velocity (\(v_{y,i}\)):
Hint: Use \(v_{y,f} = v_{y,i} - g \cdot t_{peak}\), where \(v_{y,f} = 0\).
C. Calculate maximum height (\(y_{max}\)):
Formula: \(y_f = y_i + v_{y,i} \cdot t_{peak} - \frac{1}{2}g(t_{peak})^2\)
Analysis
1. How did your calculated max height compare to your visual estimate?
2. List two sources of error that might make your calculated height different from the true height.
Skyward Bound Journal Prompts Physics Reflection Journal
Entry: Projectile Independence
Student Name
Launch Date
01. The Vertical "Freeze"
In our warm-up and the dumpling video, we observed that vertical velocity is zero at the peak. Explain in your own words why this must happen before the object begins to fall.
02. Gravity's One-Way Grip
Why does gravity only affect the vertical velocity of your water balloon and not its horizontal velocity? (Think about the direction of the force vector for gravity).
Key Insight: Horizontal motion is "inertial" (constant velocity) because there is no horizontal force, while vertical motion is "accelerated" because of the downward force of gravity.
Skyward Bound Teacher Guide Teacher Guide: Skyward Bound
11th Grade Physics | Projectile Motion Launch Lab
Material Checklist
Water Balloons (Pre-filled, medium size)
3-Person Slingshot or Mechanical Launcher
Large Protractor (for launch angle)
Stopwatches (1 per student group)
Measuring Tape (or pre-marked 1m lines)
Clipboards & Skyward Bound Worksheets
Safety Protocol
Ensure a clear launch zone of at least 30 meters.
No students permitted downrange during launches.
Launching team must wear eye protection.
Wait for "Clear" signal before each launch.
Setup Instructions
Launcher Alignment
Mount the large protractor to the center of the launcher's pivot or have a student hold it against the launch cord. Ensure 0° is parallel to the ground.
Timing Technique
Assign one student per group as the "Timer." They must stand perpendicular to the flight path to clearly see the launch and impact.
Lesson Pacing
Warm-up 5 min
Video Analysis 15 min
Launch Activity 20 min
Journal/Cleanup 10 min
Differentiation & Support
Scaffolding
For students struggling with algebra, provide a "Step-by-Step" calculation card that has the numbers plugged in for a sample 4-second flight.
Extension
Challenge advanced students to calculate the horizontal distance based on their time and the launch angle (\(\cos\theta\)).