Using the formula: H = (u² * sin²θ) / (2g). H = (20² * (1/2)) / (2 * 9.8) = 10.2 m, approximately 10 m.

Maximum height h = (u^2 * sin²θ) / (2g) = (20² * (1/2)²) / (2 * 10) = 5 m.

Maximum height = (u^2 * sin²θ) / (2g) = (40^2 * (1/2)) / (2 * 10) = 80 m.

Maximum height (H) = (u² * sin²θ) / (2g) = (30² * (1/2)) / (2 * 9.8) = 22.5 m.

Maximum height (H) = (u² * sin²θ) / (2g). Here, u = 30 m/s, θ = 45°, g = 9.81 m/s². H = (30² * (1/2)) / (2 * 9.81) = 22.5 m.

Using Snell's law, n1 * sin(theta1) = n2 * sin(theta2). Here, n1 = 1 (air), theta1 = 45 degrees, n2 = 1.5 (glass). Thus, sin(theta2) = (1 * sin(45))/1.5 = 0.471, giving theta2 ≈ 30 degrees.

When a ray passes through the center of curvature, it reflects back on itself, forming a real and inverted image at the same distance as the object.

Using Snell's law, n1 * sin(i) = n2 * sin(r). Here, n1 = 1 (air), i = 30 degrees, n2 = 1.5 (glass). Therefore, sin(r) = (1 * sin(30))/1.5 = 0.333. Thus, r = sin^(-1)(0.333) ≈ 19.5 degrees, which is approximately 20 degrees.

According to the law of reflection, the angle of reflection is equal to the angle of incidence. Therefore, the angle of reflection is 30 degrees.

For maximum area, the rectangle should be a square. Thus, each side = 40/4 = 10 cm.

For maximum area, the rectangle should be a square. Thus, each side = 40/4 = 10 cm.

For a fixed perimeter, the area is maximized when the rectangle is a square. Thus, side = 10 units.

For maximum area, the rectangle should be a square. Thus, each side = 40/4 = 10.

COP = T_cold / (T_hot - T_cold) = 250 K / (300 K - 250 K) = 250 / 50 = 5.0.

COP = Q_in / W = 200 J/s / (250 J/s - 200 J/s) = 200 / 50 = 4.

COP = Q_c / W = 200 J/s / (250 J/s - 200 J/s) = 200 / 50 = 4.

COP = Qc/W, thus W = Qc/COP = 200 W / 4 = 50 W.

Capacitive reactance Xc = 1/(2πfC) = 1/(2π(50)(100 × 10^-6)) ≈ 3.18 Ω.

Power (P) is given by P = V^2/R = 20V^2 / 10Ω = 400W / 10 = 40W.

Power (P) is given by P = V^2/R = (20V)^2 / 10Ω = 400/10 = 40W.

Power (P) is given by P = V^2/R = (20V)^2 / 10Ω = 400/10 = 40W.

New angular momentum L' = I'ω' = (2I)(ω/2) = L.

Angular momentum L is given by L = Iω, thus ω = L/I.

Rotational kinetic energy K.E. = (1/2)Iω².

The rotational kinetic energy is given by KE = 0.5 I ω² = 0.5 * 3 * (4)² = 24 J.

The rotational kinetic energy is given by KE = (1/2)Iω² = (1/2)(5 kg·m²)(4 rad/s)² = 40 J.

L = Iω, if I is halved and ω is doubled, L' = (1/2)(2ω) = L.

Average velocity = total distance / total time = 400 m / 50 s = 8 m/s.

Average velocity = total displacement / total time. Since the runner returns to the starting point, displacement = 0. Average velocity = 0 m/s.

Gravitational force is inversely proportional to the square of the radius. If radius is tripled, force becomes 1/3² = 1/9.