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📅 May 16, 2026 👤 scraface

May 16, 2026

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📌 Total retention sum = (78 × 40) + (65 × 40) = 3120 + 2600 = 5720. Total students = 80. Weighted average = 5720 / 80 = 71.5%.

📌 In a particle detector, a muon travels at 0.98c. Using the Lorentz factor γ = 1 / √(1 − v²/c²), calculate γ to three significant figures.

📌 v = 0.98c → v²/c² = 0.9604. Then 1 − v²/c² = 1 − 0.9604 = 0.0396. √0.0396 ≈ 0.199. γ = 1 / 0.199 ≈ 5.03.

📌 A physics educator models the trajectory of a projectile launched at 30 m/s at 30° above horizontal. What is the maximum height reached? (Use g = 9.8 m/s², and ignore air resistance.)

📌 Vertical velocity = 30 × sin(30°) = 30 × 0.5 = 15 m/s. At maximum height, final vertical velocity = 0. Using v² = u² − 2gh → 0 = 15² − 2×9.8×h → 225 = 19.6h → h = 225 / 19.6 ≈ 11.48 m.

📌 A biologist collaborating with a physicist models diffusion of ions in a cell membrane. The mean squared displacement after t seconds is given by ⟨r²⟩ = 2Dt, where D = 5 × 10⁻¹¹ m²/s. What is ⟨r²⟩ after 2000 seconds?

📌 ⟨r²⟩ = 2 × (5 × 10⁻¹¹) × 2000 = 10⁻¹¹ × 2000 = 2 × 10⁻⁸ m².

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