Stunt Park Math

Station 3

Zip Line Distance & Velocity

Pacing: 19:00 – 26:00

Flight Path Dimensions

Right Triangle Cable Span

Horizontal Run (\(a\)): 80.0 Meters

Vertical Drop (\(b\)): 24m − 6m = 18.0 Meters

Test Run Transit Time (\(t\)): 5.0 Seconds

Formulas: \(c = \sqrt{a^2 + b^2}\)  |  \(v_{\text{avg}} = \frac{c}{t}\)

Velocity Audit Tasks

• 1. Find true diagonal cable distance \(c\) using Pythagoras.
• 2. Calculate average velocity in meters per second (m/s).
• 3. Convert velocity to km/h (\(\times 3.6\)). Is it within the 60 km/h limit?

🛑 Braking Clearance: Magnetic catch requires ≥ 15m runout buffer.

Dossier: Complete Station 3 on Page 1 Cable Distance \(\approx 82.0\text{ m}\) • Speed \(\approx 16.4\text{ m/s}\) (59.0 km/h)

Synthesis

Layout Audit: Alpha vs. Beta

Pacing: 26:00 – 29:00

Layout Alpha

FLAW DETECTED

• Archery Range: Pointed toward access path with only 6° safety clearance (Code requires ≥ 15°).

• Zip Line Braking: Landing zone is 8m before perimeter fence (Code requires ≥ 15m).

• Bounce Pad: Positioned adjacent to zip line support anchor (collision risk).

❌ Fails State Safety Inspection

Layout Beta

OPTIMIZED

• Archery Range: Oriented into reinforced earth berm with 22° clear margin.

• Zip Line Braking: Full 18m straight-line runout with emergency magnetic arrestor.

• Bounce Pad: 12m perimeter fall buffer with padded perimeter zone.

✅ Meets 100% Code Compliance

Turn to Page 2 of your Inspector Dossier Verify compliance checks and state your engineering rationale!

Final Certification & Debrief

Final 60 Seconds

Inspector Sign-Off Protocol

Before submitting your dossier, make sure both engineering inspectors have signed the certification stamp and verified all three mathematical tolerances.

Archery Angle

2.9° Elevation

Max Bounce Force

4,508 N (<5 kN)

Zip Cable Speed

16.4 m/s (59 km/h)

Apex Stunt Park Engineering Review Submit Dossier to Lead Inspector (Teacher)

Engineering Audit: Plan a Safe Setup

Phase 2: Layout Optimization

Compare two proposed park configurations against municipal safety codes. Calculate angular clear-zones, runout braking margins, and fall perimeter buffers to identify the compliant blueprint.

Layout Alpha (Current Draft)

Option A

🎯 Archery Direction: Toward East Fence

• Overshoot safety angle cone: 8° from centerline
• Lateral distance to main pedestrian pathway: 5.5 m

🚡 Zip Line Landing: 8.0 m Braking Runout

• Distance from brake trolley to boundary fence: 8.0 m

🎪 Bounce Pad Buffer: 4.5 m Perimeter

• Clearance to adjacent zip line steel anchor: 3.0 m

Layout Beta (Proposed Revision)

Option B

🎯 Archery Direction: Toward North Berm

• Overshoot safety angle cone: 22° into earth berm
• Lateral distance to pedestrian pathway: 28.0 m

🚡 Zip Line Landing: 18.0 m Braking Runout

• Distance from brake trolley to boundary fence: 18.0 m

🎪 Bounce Pad Buffer: 10.0 m Perimeter

• Clearance to nearest structure/tower: 12.0 m

1. Braking Distance Safety Check:

At \(16.4\text{ m/s}\), magnetic braking requires stopping distance \(d_{\text{stop}} = \frac{v^2}{2a}\). With emergency deceleration \(a = 12\text{ m/s}^2\), calculate minimum safe runout distance (\(d_{\text{stop}} = \frac{16.4^2}{24} = \frac{269}{24}\)). Which layout provides adequate clearance?

2. Archery Angle Clearance Check:

State code mandates a minimum safety overshoot cone angle of ≥ 15.0° on both sides of target line without pedestrian foot traffic. Which layout satisfies this code? Show evidence:

Safety Code Audit Matrix

Final Inspector Determination Official Municipal Sign-off

I hereby recommend [   ] Layout Alpha     [   ] Layout Beta for official park construction.

Engineering Justification (Cite mathematical proof from calculations above):

Lead Inspector Signature: ____________________________ Clearance Status: [   ] APPROVED   [   ] REJECTED

Apex Safety Engineering • Field Verification Page 2 of 2

2. Archery Angle Clearance Verdict:

• Layout Alpha: \(8.0^\circ\) clear cone < \(15.0^\circ\) mandated standard → FAIL (Path is only 5.5m away).
• Layout Beta: \(22.0^\circ\) clear cone ≥ \(15.0^\circ\) mandated standard → PASS (Targets point safely into earth berm).

Final Inspector Approval: LAYOUT BETA IS APPROVED. Students must cite at least two mathematical proofs (e.g. \(11.2\text{ m} > 8\text{ m}\) braking hazard, and \(22^\circ \ge 15^\circ\) archery clearance) for full credit.

Apex Engineering Solutions Key • Total Score: 20 Points Confidential Teacher Material