Projectile Drop Lab Handout
Conceptual Readiness
Horizontal Projectiles: Pre-Lab Concepts
Physical Principles, Kinematic Formulas & Experimental Variables (Complete before simulation)
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Date: Period:
Core Principle: Independence of Horizontal and Vertical Motion Galileo's Orthogonal Independence
When an object is launched horizontally from an elevation with negligible air drag:
Horizontal Dimension (\(x\)): Zero horizontal force (\(a_x = 0\)). Constant horizontal velocity: \(v_x = v_0\).
Vertical Dimension (\(y\)): Constant gravitational acceleration (\(a_y = -g\)). Free fall from rest: \(v_{0y} = 0\).
\(v_x\) constant \(v_y\) accelerates
Part 1: Conceptual Predictions & Kinematic Formulation
1. Dropped vs. Fired Horizontally: Ball A is dropped from rest at height \(h\). At the same instant, Ball B is fired horizontally at high speed from height \(h\). Neglecting air resistance, which ball hits the ground first? Explain why.
2. Impact of Launch Speed on Fall Time: If you increase horizontal speed (\(v_0\)) while keeping elevation (\(h\)) constant, does flight time increase, decrease, or remain constant?
3. Mass Independence: If a light ball and a heavy ball are fired horizontally with the same speed from the same height in a vacuum, will their landing ranges differ? Why?
4. Directional Formulas & Combined Form for Range (\(x\)): Write the kinematic equation for each direction, then combine them to eliminate time (\(t\)) to solve only for \(x\):
Horizontal (\(x\)-direction):
\(x =\)
Vertical (\(y\)-direction):
\(h =\)
Combined Form for \(x\):
\(x =\)
Prediction: How should \(x\) scale with \(v_0\) in Part A? How should \(x\) scale with \(h\) in Part B?
Part 2: Experimental Variable Identification (Student Fill-In)
Fill in the physical variables for both experimental parts
In Part A you will vary launch velocity \(v_0\) and measure range \(x\). In Part B you will vary height \(h\) and measure range \(x\). Identify each variable:
| Variable Category | Part A: Vary Launch Speed (\(v_0\)), Measure Range (\(x\)) | Part B: Vary Elevation Height (\(h\)), Measure Range (\(x\)) |
|---|
| Independent Variable (IV) | | |
| Dependent Variable (DV) | | |
| Controlled Variable 1 | | |
| Controlled Variable 2 | | |
| Unmeasured Variable | | |
Physics Mechanics: Pre-Simulation Conceptual Foundations Page 1 of 2
Projectile Drop Lab | Post-Lab Conceptual Synthesis: Part A & Part B
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Part A: Varying Launch Velocity (\(v_0\)) with Constant Height (\(h\))
1. Proportionality: Did your experimental data confirm a direct linear relationship between range \(x\) and launch speed \(v_0\)? If speed was doubled from \(10\text{ m/s}\) to \(20\text{ m/s}\), by what factor did range increase?
2. Fall Time Invariance: Since you held height \(h\) constant during Part A, did changing the launch velocity affect how long the projectile remained in the air? Explain how this proves horizontal and vertical motions are independent.
Part B: Varying Elevation Height (\(h\)) with Constant Velocity (\(v_0\))
3. Non-Linear Scaling: When you increased cannon height from \(5\text{ m}\) to \(20\text{ m}\) (a \(4\times\) increase), did the range quadruple? Based on kinematic principles, by what factor should the range actually increase? Explain why:
4. Vertical Drop & Flight Time: Unlike Part A, did changing the elevation in Part B alter the total flight time? Explain physically why height dictates the time of flight while horizontal speed does not.
Part C: Determining Acceleration Due to Gravity (\(g\))
5. Calculating Gravity from Part 2 Data Only: How can you calculate the acceleration due to gravity (\(g\)) using only your measurements and parameters from Part 2 (where height \(h\) was varied and launch velocity \(v_0\) was constant)? Explain your physical reasoning, write the equations you would use, show your algebraic steps, and state your final derived formula for \(g\):
Show reasoning & algebraic steps:
Final Formula for \(g\):
\(g =\)
In terms of \(h\), \(x\), and/or \(t\)
Part D: Real-World Complications (Enabling Air Drag)
Impact on Horizontal Velocity:
With air drag ON, does horizontal velocity \(v_x\) stay constant? What force acts horizontally, and how does this affect final range?
Trajectory Asymmetry:
Does the path remain a symmetric parabola with drag? Describe how the trajectory steepens near the ground.
Physics Mechanics: Post-Laboratory Synthesis & Evaluation Page 2 of 2
Projectile Drop Answer Key
Teacher Guide & Answer Key
Horizontal Projectiles: Pre-Lab Answer Key
Exemplary Conceptual Responses, Variable Mapping & Misconception Guidance
For Educator Use Only AP / Honors / General Physics
Pedagogical Focus: Ensure students complete Page 1 before accessing laptops. Emphasize that \(v_x\) has zero impact on vertical free fall.
Part 1: Conceptual Predictions & Formulas
1. Dropped vs. Fired Horizontally: They strike the ground simultaneously (at the exact same time).
Exemplary Explanation: Vertical motion is completely independent of horizontal motion. Both balls start with zero initial vertical velocity (\(v_{0y} = 0\)) and experience the identical downward acceleration due to gravity (\(a_y = -g = -9.81\text{ m/s}^2\)) from the same height (\(h\)). Because \(h = \frac{1}{2}gt^2\), both require the exact same fall time \(t = \sqrt{2h/g}\).
2. Impact of Launch Speed on Fall Time: Flight time remains unchanged (constant).
Exemplary Explanation: Changing horizontal velocity (\(v_0\)) only alters horizontal displacement (\(x = v_0 t\)). Since gravity only accelerates objects vertically and \(v_{0y} = 0\), the time to fall \(10\text{ m}\) is determined solely by \(h\) and \(g\), not \(v_0\).
3. Mass Independence: Landing ranges will be identical.
Exemplary Explanation: In Newton's second law, gravitational force is \(F_g = mg\), so acceleration is \(a = F_g / m = (mg)/m = g\). Mass cancels out of all kinematic trajectory equations in a vacuum, so trajectories are identical.
4. Directional Formulas & Combined Form for Range (\(x\)):
Horizontal: \(x = v_0 \cdot t\)
Vertical: \(h = \frac{1}{2} g t^2\)
Combined Form: \(x = v_0 \sqrt{\frac{2h}{g}}\)
Physical Scaling: In Part A (\(h\) constant), \(x \propto v_0\) (linear proportionality). In Part B (\(v_0\) constant), \(x \propto \sqrt{h}\) (square root relationship).
Part 2: Completed Variable Identification Table
| Variable Category | Part A: Vary Speed (\(v_0\)), Fixed Height (\(h\)) | Part B: Vary Height (\(h\)), Fixed Speed (\(v_0\)) |
|---|
| Independent (IV) | Horizontal Velocity (\(v_0\)) | Elevation Height (\(h\)) |
| Dependent (DV) | Horizontal Range (\(x\)) | Horizontal Range (\(x\)) |
| Controlled Variable 1 | Height (\(h = 10.0\text{ m}\) constant) | Speed (\(v_0 = 15.0\text{ m/s}\) constant) |
