Explain Newton's Second Law of Motion and calculate the common velocity of a boy and skateboard after the boy jumps onto it, given their masses and initial velocities.

You're on a roll — here are the solutions to your questions: 8. a) Newton's Second Law of Motion states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The direction of the acceleration is in the direction of the net force. Mathematically, this is expressed as F = ma. b) This question is incomplete due to the blurry image. Please provide the full text for me to answer it. c) To determine the common velocity of the boy and the skateboard: Step 1: Identify the given values. Mass of boy, m_1 = 50 kg Initial velocity of boy, u_1 = 2 m/s Mass of skateboard, m_2 = 5 kg Initial velocity of skateboard, u_2 = 0 m/s (assuming it starts from rest) Let the common final velocity be v. Step 2: Apply the principle of conservation of momentum. The total momentum before the collision equals the total momentum after the collision. m_1 u_1 + m_2 u_2 = (m_1 + m_2) v Step 3: Substitute the values into the equation. (50 kg)(2 m/s) + (5 kg)(0 m/s) = (50 kg + 5 kg) v 100 kg m/s + 0 = (55 kg) v 100 kg m/s = 55 kg · v Step 4: Solve for v. v = 100 kg m/s55 kg v ≈ 1.82 m/s 13. a) Refraction of light is the bending of light as it passes from one transparent medium to another, due to a change in its speed. b) To determine the refractive index of water with respect to air: Step 1: Identify the angles from the diagram. Angle of incidence in air, _air = 42^ Angle of refraction in water, _water = 30^ The refractive index of air, n_air ≈ 1. Step 2: Apply Snell's Law. n_air _air = n_water _water Step 3: Substitute the known values. 1 × 42^ = n_water × 30^ Step 4: Calculate the sine values. 42^ ≈ 0.6691 30^ = 0.5 Step 5: Solve for n_water. 0.6691 = n_water × 0.5 n_water = (0.6691)/(0.5) n_water = 1.3382 Got more? Send 'em!