Projectile Motion Lab: Virtual Experiment Guide
If you are a student writing a lab report or a teacher looking for a ready-to-use virtual activity, follow this structured laboratory procedure to collect data and verify the fundamental laws of kinematics.
If you are a student writing a lab report or a teacher looking for a ready-to-use virtual activity, follow this structured laboratory procedure to collect data and verify the fundamental laws of kinematics.
Experiment 1: Investigating Launch Angle vs. Horizontal Range
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Objective: Determine the mathematical relationship between the launch angle and the maximum horizontal distance traveled.
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Controlled Variables: Initial Speed = 30 m/s, Gravity = 9.8 m/s² (Earth), Launch Height = 0 m.
Procedure:
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Set the initial speed to 30 m/s and launch height to 0 m.
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Use the slider to set the launch angle to 15°. Click Launch! and record the Range (m).
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Click Reset, change the angle to 30°, and launch again.
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Repeat for 45°, 60°, and 75°. 5. Pro Tip: Click the "Compare 5 angles" button in the simulator to visually superimpose all five trajectories instantly!
Launch Angle (°) | Initial Speed (v0) | Gravity (g) | Theoretical Range (m) | Simulated Range (m) | Flight Time (s) |
|---|---|---|---|---|---|
15° | 30 m/s | 9.8 m/s² | 45.9 | Verify in simulator | Verify in simulator |
30° | 30 m/s | 9.8 m/s² | 79.5 | Verify in simulator | Verify in simulator |
45° | 30 m/s | 9.8 m/s² | 91.8 | Verify in simulator | Verify in simulator |
60° | 30 m/s | 9.8 m/s² | 79.5 | Verify in simulator | Verify in simulator |
75° | 30 m/s | 9.8 m/s² | 45.9 | Verify in simulator | Verify in simulator |
The Physics Behind Projectile Motion (Core Kinematics)
A projectile is any object thrown, kicked, or launched into space that is acted upon only by the acceleration of gravity. To accurately predict where the projectile will land, we split its two-dimensional motion into two entirely independent, one-dimensional vectors: horizontal motion (constant velocity) and vertical motion (constant acceleration).
1. Resolving the Initial Velocity Vectors
Before calculating flight paths, the initial launch velocity must be broken into its horizontal (vₓ) and vertical (vᵧ) components using basic trigonometry:
vₓ = v₀ cos(θ)
vᵧ = v₀ sin(θ)
2. Horizontal Motion (No Air Resistance)
Because we assume air resistance is negligible in this simulator, there is zero horizontal acceleration (aₓ = 0). The horizontal distance (displacement) at any timestamp (t) is strictly linear:
x(t) = vₓ · t = v₀ cos(θ) · t
3. Vertical Motion (Gravitational Acceleration)
The vertical path is governed by constant gravitational acceleration (aᵧ = -g), which pulls the object downward back to Earth. The vertical position at any time (t) is calculated using the classic kinematic equation:
y(t) = y₀ + v₀ sin(θ) · t - ½gt²
4. Solving for Key Metrics
When conducting your projectile motion lab, you can check your manual calculations against the simulator using these definitive formulas:
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Time of Flight (t_land on flat ground): Derived by setting y(t) = 0: t_land = [ 2v₀ sin(θ) ] / g
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Maximum Peak Height (H_max): Occurs exactly when vertical velocity drops to zero (vᵧ = 0): H_max = y₀ + [ (v₀ sin(θ))² ] / 2g
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Maximum Horizontal Range (R): Found by multiplying horizontal velocity by total flight time: R = [ v₀² sin(2θ) ] / g
Frequently Asked Questions (FAQ)
Q: Which launch angle yields the maximum horizontal range?
A: On perfectly flat ground (y₀ = 0), a launch angle of 45° always yields the maximum possible horizontal range. This is because sin(2θ) reaches its absolute maximum value of 1 when 2θ = 90°, which means θ = 45°. If you increase the initial launch height (y₀ > 0), the optimal angle shifts slightly below 45°.
Q: How does changing gravity affect the projectile's trajectory?
A: Gravitational acceleration only affects the vertical component of motion. Higher gravity (like Jupiter at 24.8 m/s²) rapidly halts upward vertical velocity and pulls the projectile down faster, resulting in a much shorter flight time and restricted horizontal range. Lower gravity (like the Moon at 1.6 m/s²) allows the projectile to float extensively, covering massive distances.
Q: Why do angles like 30° and 60° land at the exact same horizontal distance?
Complementary launch angles (angles that add up to 90°) will always achieve the exact same horizontal range on flat ground. Mathematically, sin(2 × 30°) = sin(60°) and sin(2 × 60°) = sin(120°) yield the identical numeric result. However, notice that the 60° launch achieves a much higher peak height and spends significantly more time in the air!
Free Projectile Motion Lab Guide & Printables
Download Free Projectile Motion Lab Worksheet (PDF) by clicking the image above