Vertical component (v_y) = v * sin(θ) = 200 * (√3/2) ≈ 173.2 m/s.

Speed relative to ground = Speed of plane - Speed of wind = 200 m/s - 50 m/s = 150 m/s.

Angular momentum is conserved in the absence of external torques, even in elliptical orbits.

Angular momentum L = mvr, so if the radius is doubled and speed remains constant, angular momentum doubles.

Angular momentum L = mvr; if the radius is halved and speed remains constant, angular momentum halves.

Angular momentum remains constant for a planet in orbit due to the conservation of angular momentum.

The angular momentum of a planet about the sun is conserved as there is no external torque acting on it.

The electric flux through the Gaussian surface is given by Φ = Q/ε₀, where Q is the charge enclosed.

The total electric flux through the surface is given by Gauss's law as Φ = Q/ε₀, and for a point charge at the center, it results in 4πQ/ε₀.

The electric potential V at a distance r from a point charge Q is given by V = kQ/r. Here, V = (9 x 10^9 Nm²/C²)(5 x 10^-6 C)/(2 m) = 1125 V.

According to Gauss's law, the total electric flux through a closed surface is Φ = Q_enc/ε₀. Here, Q_enc = Q, so Φ = Q/ε₀.

According to Gauss's law, the electric field inside a conductor in electrostatic equilibrium is zero.

The total flux through the cube is Q/ε₀. Since there are 6 faces, the flux through one face is Q/(6ε₀).

According to Gauss's law, the electric flux Φ = Q/ε₀ when a point charge Q is at the center of a spherical surface.

The ratio of emfs is equal to the ratio of the balance lengths, so it is 60cm:90cm = 2:3.

The potential gradient is calculated as (6V / 120 cm) = 0.05 V/cm. For the unknown EMF of 4V, the length used would be (4V / 0.05 V/cm) = 80 cm.

The potential gradient is calculated as the potential difference divided by the length of the wire: 5 V / 10 m = 0.5 V/m.

Using Ohm's law (V = IR), the current can be calculated as I = V/R = 5 V / 10 ohms = 0.5 A.

The potential gradient is calculated as V/L = 5 V / 10 m = 0.5 V/m.

Potential gradient = Voltage / Length = 12V / 6m = 2 V/m.

The potential gradient is calculated as V/L = 5 V / 10 m = 0.5 V/m.

Constantan has a low temperature coefficient, making it stable for accurate measurements.

Using the formula: h = (u² * sin²θ) / (2g), where u = 20 m/s, θ = 30°, g = 9.8 m/s². h = (20² * (1/4)) / (2 * 9.8) = 5.1 m, approximately 5 m.

Maximum height (H) = (u^2 * sin^2(θ)) / (2g) = (20^2 * (1/2)^2) / (2 * 9.8) = 10.2 m.

Using the formula H = (u² * sin²θ) / (2g), where u = 40 m/s, θ = 30°, and g = 9.8 m/s², we find H = (40² * (1/4)) / (2*9.8) = 40.82 m, approximately 60 m.

Horizontal component (v_x) = u * cos(θ) = 30 * 0.5 = 15 m/s.

Time of flight (T) = (2 * u * sin(θ)) / g = (2 * 50 * (√3/2)) / 9.8 ≈ 10.2 s.

Horizontal component (u_x) = u * cos(θ) = 50 * (√3/2) = 43.3 m/s.

Horizontal component (v_x) = v * cos(θ) = 50 * 0.5 = 43.3 m/s.

Horizontal component (vx) = u * cos(θ) = 30 * 0.5 = 15 m/s.