Explanation

Range of projectile: R = (v² sin2θ) / g

Doubling speed: v → 2v → R_new = (4v² sin2θ) / g = 4R.

Explanation

Distance traveled along semicircle = π × r = π × 10 = 31.42 m

Displacement = straight line along diameter = 2 × r = 20 m → Ratio = π : 2.

Explanation

Force in a medium: F = F₀ / εᵣ, where εᵣ = relative permittivity

F = 28 / 2.8 = 10 N.

Explanation

Inductive reactance: X_L = 2πfL

If frequency f is doubled, X_L doubles.

Explanation

Work done at constant pressure: W = P × ΔV

ΔV = 3 – 1 = 2 m³, P = 2 Pa

W = 2 × 2 = 4 J

Positive work → gas does work on surroundings.

Explanation

Interference occurs when waves overlap and combine constructively or destructively.

Requires coherent sources (same frequency and constant phase difference).

Explanation

Use Newton’s 2nd law: F = m Δv/Δt

Δv = 10 – 20 = –10 m/s, m = 150 kg, Δt = 3 s

F = 150 × (–10 / 3) ≈ –500 N

Magnitude of braking force = 500 N.

Explanation

In a displacement-time graph, slope = velocity.

Straight line → slope constant → velocity remains constant.

Explanation

Use the formula: cosθ = (A · B) / (|A||B|)

A · B = (2)(-6) + (3)(4) = -12 + 12 = 0

|A| = √(2² + 3²) = √13, |B| = √((-6)² + 4²) = √52

cosθ = 0 / (√13 × √52) = 0 → θ = 90°

Explanation

For opposite charges, electric fields point toward negative and away from positive.

Between them, the fields add up, so no point exists where the net field is zero.