#### 71.5

February 22, 2026

#### 71.5

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The beam spreads 0.5 mm per meter, so after 8 meters, it spreads by 0.5 × 8 = 4 mm. Initial diameter is 2 mm, so total width is 2 + 4 = 6 mm.
An educational psychologist compares learning retention rates between two groups: one using virtual labs (78% retention, 40 students) and one using textbooks (65% retention, 40 students). What is the weighted average retention rate across both groups?
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.)

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