According to Newton's Third Law of Motion and the Law of Conservation of Momentum, when a gun exerts a forward force on a bullet, the bullet exerts an equal and opposite force on the gun. Consequently, the gun experiences a backward velocity known as recoil. Since the system is isolated, the total momentum remains zero, meaning the magnitude of the gun's momentum equals the magnitude of the bullet's momentum.

Impulse is defined as the change in momentum, which is equal to the average force multiplied by the time interval of the impact. A helmet increases the time duration of the collision, which effectively reduces the average force exerted on the head. While the total change in momentum (impulse) is technically the same, the helmet reduces the peak force, often described in this context as reducing the impulsive impact.

Using Newton's Second Law in terms of momentum: F = Δp / Δt = m(v - u) / Δt. Given m = 0.1 kg, v = 0, u = 30 m/s, and Δt = 0.05 s, the force is 0.1 * (0 - 30) / 0.05 = -3 / 0.05 = -60 N. The negative sign indicates the force opposes the initial motion.

A jet engine operates by expelling high-velocity exhaust gases backward. According to the law of conservation of linear momentum, the momentum gained by the exhaust gases in one direction must be balanced by an equal and opposite momentum gained by the engine, creating forward thrust.

Linear momentum (p) is the product of an object's mass (m) and its velocity (v), expressed as p = m * v. By multiplying 14 kg by 28 m/s, we obtain 392 kg·m/s, which represents the total momentum of the object.

The impulse (change in momentum) is the same for both eggs. Impulse = Force × time. The pillow increases the impact time, significantly reducing the peak force exerted on the egg, preventing it from breaking. The floor results in a very short impact time, leading to a large force that breaks the egg. Option B is unlikely as the pillow is designed to prevent breakage.

Linear momentum is a fundamental vector quantity in classical mechanics defined as the product of an object's mass and its velocity (p = mv). It quantifies the 'quantity of motion' an object possesses. Therefore, both the mass of the object and its velocity are essential factors in determining its total momentum.

Newton's Second Law of Motion states that the net force acting on an object is directly proportional to the rate of change of its momentum. Mathematically, F = dp/dt, where p is momentum and t is time. Therefore, the rate of change of momentum is exactly equal to the resultant force applied to the body.

A safety helmet is designed to increase the duration of the impact during a collision. According to the impulse-momentum theorem, impulse is the product of force and time. By extending the time over which the change in momentum occurs, the helmet reduces the average impact force exerted on the head, thereby minimizing the risk of injury.

Using the law of conservation of momentum: m1*v1 + m2*v2 = 0. Converting 20g to 0.02kg: (0.02 * 150) + (3 * V) = 0. Thus, 3 + 3V = 0, which gives V = -1.0 m/s. The negative sign indicates the direction of recoil is opposite to the bullet's motion.