91Ó°ÊÓ

Momentum is a fundamental concept in physics, describing the quantity of motion an object has. Momentum is defined as the product of an object's mass and velocity, represented by the formula: \( p = mv \). Here, 'p' is momentum, 'm' is mass, and 'v' is velocity.

In the problem, each bullet has a mass of \(3 \text{ g} \) or \(0.003 \text{ kg} \) and a speed of \(500 \text{ m/s} \). Using the momentum formula, we calculated the momentum of one bullet to be: \[ p = 0.003 \times 500 = 1.5 \text{ kgâ‹…m/s} \]

Understanding momentum helps us analyze changes in motion when objects interact. In this scenario, the gangster’s bullets hit and bounce back from Superman's chest without slowing down, leading to a reversal in momentum.

Force is what causes an object to accelerate, and it is calculated using Newton’s second law of motion, which states that force is equal to the rate of change of momentum. The formula is: \( F = \frac{ \triangle p }{ \triangle t } \) where \( \triangle p \) is the change in momentum and \( \triangle t \) is the time interval.

In the exercise, each bullet changes its momentum when it bounces back. The initial momentum is \(1.5 \text{ kgâ‹…m/s} \) and the final momentum is \(-1.5 \text{ kgâ‹…m/s} \). Therefore, the change in momentum for one bullet is: \[ \triangle p = p_{ \text{ final }} \text{ - } p_{ \text{ initial }} \text{ = } (-1.5) - 1.5 = -3 \text{ kgâ‹…m/s} \]

Given 100 bullets per minute, the total change in momentum per minute is \(-300 \text{ kg⋅m/s} \). Converting this into seconds, the average force on Superman’s chest is: \[ F_{ \text{ avg }} = \frac{ -300 }{ 60 } = -5 \text{ N} \] The magnitude of which is \(5 \text{ N} \).

Projectile motion describes the motion of an object thrown or projected into the air, subject to only the acceleration of gravity. In this exercise, bullets are moving towards Superman's chest, and they follow a linear path due to the high speed and close range.

For projectile motion, key factors include initial velocity, angle of projection, and effects of gravity. Even if the bullets aren't falling freely, understanding projectile motion helps grasp how objects move when launched. Each bullet has a speed of \(500 \text{ m/s} \) and travels in a straight line towards Superman before rebounding.

Factors like air resistance and trajectory can influence projectile motion, but with bullets and a direct path, these effects are minimal. Hence, this problem simplifies to linear motion with a rebound effect, aligning with fundamental projectile motion concepts.