Question 1

How do I calculate projectile motion (range and height)?

Accepted Answer

Projectile motion formulas: Range R = v₀² × sin(2θ) / g. Maximum height H = v₀² × sin²(θ) / (2g). Time of flight T = 2v₀ × sin(θ) / g. Where v₀ is initial velocity (m/s), θ is launch angle (degrees), and g = 9.81 m/s². Air resistance is neglected in standard calculations.

Question 2

What is the formula for the period of a simple pendulum?

Accepted Answer

Period T = 2π × √(L/g), where L is pendulum length (m) and g = 9.81 m/s² (gravitational acceleration). This approximation is valid for small angles (θ < 15°). For large angles, T = 2π × √(L/g) × (1 + θ²/16 + ...). Frequency f = 1/T Hz.

Question 3

How do you calculate wave speed, frequency and wavelength?

Accepted Answer

Wave equation: v = f × λ, where v is wave speed (m/s), f is frequency (Hz), and λ is wavelength (m). For sound in air: v ≈ 343 m/s at 20°C. For electromagnetic waves: v = c = 3 × 10⁸ m/s. Energy of a photon: E = hf = hc/λ, where h = 6.626 × 10⁻³⁴ J·s (Planck's constant).

Question 4

What is Snell's Law in optics?

Accepted Answer

Snell's Law: n₁ × sin(θ₁) = n₂ × sin(θ₂), where n₁ and n₂ are the refractive indices of the two media, and θ₁ and θ₂ are the angles of incidence and refraction measured from the normal. Total internal reflection occurs when θ₁ > θc = arcsin(n₂/n₁) for n₁ > n₂.

Question 5

How do you calculate relativistic mass-energy equivalence?

Accepted Answer

Einstein's mass-energy equivalence: E = mc², where E is energy (Joules), m is mass (kg), and c = 2.998 × 10⁸ m/s. For moving objects, total energy E = γmc², where Lorentz factor γ = 1/√(1 - v²/c²). Kinetic energy KE = (γ - 1)mc². At v << c, this reduces to classical KE = ½mv².

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