← The Thinking Experiment 🎯 Physics Inquiry Lab

Projectiles: Target Intercept & Kinematics Studio

Explore 2D kinematics across three curated investigations: the classic Feed the Monkey free-fall intercept, Mark Rober's motorized dartboard tracking challenge, and the classroom Cornell T-Chart cliff and obstacle analysis from lecture notes.

💡 What You Can Do in This Lab

🐵 1. Feed the Monkey Intercept Challenge

Question: Where should you aim a banana to feed a falling monkey that releases its branch the instant the cannon fires?

Turn on Line of Sight or click Auto-Aim to point directly at the monkey.
Launch the Banana at v₀ = 20 m/s, then 30 m/s, then 45 m/s.
Inspect the synchronized Strobes: both drop by the exact same distance Δy = ½gt² from the line of sight!

🎯 2. Mark Rober's Automated Dartboard

Question: How does Mark's motorized target guarantee a bullseye, and will the dart clear the workshop ceiling?

Click Load Worksheet Values (v₀ = 15.0 m/s, α = 40°, x = 5.0 m).
Watch the motorized carriage slide along the track to catch the bullseye at height H = 5.05 m.
Review Question 2: The dart apex reaches h_max = 6.45 m. Lower the ceiling slider below 6.45 m to test a ceiling collision!

📋 3. Classroom Notes (Cliff & 70m Building)

Question: A projectile is fired from a 320 m cliff at 42 m/s (30°). Does it clear the 70 m obstacle building?

Inspect the Full Solution and Cornell T-Chart: horizontal velocity is constant (v_x = 36.4 m/s) while vertical motion accelerates downward (a_y = -10 m/s²).
Find flight time to the far wall (x = 310 m): t = 8.52 s.
Verify height: y = 135.8 m > 70 m (clears roof by 65.8 m!).

📝 4. Classic 2D Trajectory Challenges

Structured Inquiry Scenarios:

Box Roll-Off: Ball rolls off 2 m box at 5 m/s. Range = 3.19 m (t = 0.64 s).
100m Cliff Launch: Lands 300 m away. Solve for launch speed: v₀ = 66.4 m/s.
Soccer Player Kick: Given v_x = 20 m/s, v_y = 12 m/s. Solve for v₀ = 23.3 m/s, θ = 31.0°, range = 49.0 m.
Tennis Serve Challenge: Serves horizontally at 40 m/s from 2.5 m. Clears 0.92 m net at 12 m (y = 2.06 m), but lands at 28.6 m > 18.4 m (Invalid / Long!).

⚙️ Investigation Scenarios:

🐵

Feed the Monkey: Free-Fall Intercept Challenge Direct sightline targeting & equal gravitational drop investigation

Problem Scenario & Physical Setup

🎯 Guided Investigation Questions 4 Questions

Speed:

📊 Live Telemetry & Kinematic State

dt = 0.01s

Elapsed Time (t)

0.00 s

Position (x, y)

(0.0, 0.0) m

Velocity (vₓ, vᵧ)

(0.0, 0.0) m/s

Total Speed (|v|)

0.0 m/s

Target Height

16.0 m

Drop Distance (½gt²)

0.00 m

📈 Kinematics Motion Graphs

Real-Time Synchronized

Horizontal Motion (x, vₓ, aₓ) Vertical Motion (y, vᵧ, aᵧ)

■ Blue Line: Horizontal (x, vₓ, aₓ) | ■ Red Line: Vertical (y, vᵧ, aᵧ)

🖱️ Click or drag graph to scrub flight time

Initial Speed (v₀): 26.0 m/s

Launch Angle (θ): 32.6°

Monkey Distance (x_m): 25.0 m

Monkey Height (y_m): 16.0 m

Cannon Height (y₀): 0.0 m

Gravity (g):

Cornell Kinematics T-Chart

Classroom Method

Horizontal (x)

aₓ = 0 m/s²

vₓ = v₀ₓ = 21.9 m/s

x = x₀ + v₀ₓ·t

x = 0.0 + (21.9)·t

Bridge

Vertical (y)

aᵧ = -g = -9.8 m/s²

vᵧ = v₀ᵧ + g·t

vᵧ = 14.0 + (-9.8)·t

y = y₀ + v₀ᵧ·t + ½gt²

y = 0.0 + (14.0)·t + ½(-9.8)·t²

Vector Decomposition (SOH CAHTOA)

                v₀ₓ = v₀ · cos(θ)
                21.9 m/s
              

                v₀ᵧ = v₀ · sin(θ)
                14.0 m/s
              

🎯 Quick Prediction Challenge

Inquiry Trial History

#	Mode	v₀ (m/s)	θ (°)	t_hit (s)	x (m)	y (m)	Result
No trial runs logged yet. Fire a projectile!