Speed of person relative to ground = Speed of train + Speed of person = 60 km/h + 4 km/h = 64 km/h.

Speed upstream = Speed of person - Speed of current = 4 km/h - 2 km/h = 2 km/h.

Speed of person relative to observer = Speed of person + Speed of escalator = 4 km/h + 2 km/h = 6 km/h.

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.

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

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.

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 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.

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

Maximum height (H) = (u^2 * sin^2(θ)) / (2g) = (20^2 * (1/2)^2) / (2 * 9.8) = 10.2 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 (v_x) = v * cos(θ) = 50 * 0.5 = 43.3 m/s.

Time of flight (T) = (2u * sin(θ)) / g = (2 * 40 * (√3/2)) / 9.8 ≈ 6.1 s.

Horizontal component (vx) = u * cos(θ) = 40 * 0.5 = 20 m/s.

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

The magnetic force is proportional to the velocity of the charge, so if the velocity is doubled, the magnetic force also doubles.

Using Snell's law, n1 * sin(θ1) = n2 * sin(θ2). Here, n1 = 1.5, θ1 = 30°, n2 = 1.0. Thus, sin(θ2) = (1.5 * sin(30°))/1.0 = 0.75, giving θ2 ≈ 60°.

Using Snell's law, n1 * sin(i) = n2 * sin(r). Here, n1 = 1 (air), i = 30 degrees, n2 = 1.5 (glass). Thus, sin(r) = (1 * sin(30))/1.5 = 0.333, giving r ≈ 18.4 degrees.

Using Snell's law, n1 * sin(θ1) = n2 * sin(θ2). Here, n1 = 1 (air), n2 = 1.33 (water), θ1 = 30 degrees. Thus, sin(θ2) = (1 * sin(30))/1.33 = 0.375. Therefore, θ2 = sin^(-1)(0.375) which is approximately 22 degrees.

Using Snell's law, n1 * sin(θ1) = n2 * sin(θ2). Here, sin(30) = 0.5, so 1 * 0.5 = 1.33 * sin(θ2). Solving gives θ2 ≈ 22.5 degrees.

Using Snell's law: n1 * sin(θ1) = n2 * sin(θ2). Here, sin(30) = 0.5, so sin(θ2) = (1 * 0.5) / 1.33 = 0.375. Thus, θ2 = sin^(-1)(0.375) ≈ 22.5 degrees.

Using Snell's law, n1 * sin(θ1) = n2 * sin(θ2). Here, n1 = 1 (air), n2 = 1.33 (water). Solving gives θ2 ≈ 22 degrees.