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Home » Simplify the expression \( rac{3^5 imes 3^-2}3^3 \). - Simpleprint

Simplify the expression \( rac{3^5 imes 3^-2}3^3 \). - Simpleprint

📅 March 13, 2026 👤 scraface

Mar 13, 2026

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📌 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.

📌 An interactive simulation shows electrons moving through a magnetic field, deflecting by a centripetal force causing circular motion. If an electron moves at 2 × 10⁶ m/s perpendicular to a 0.5 Tesla field and has a charge of 1.6 × 10⁻¹⁹ C and mass 9.1 × 10⁻³¹ kg, what is the radius of its path?

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