Fill in the Blank 16 points Two football players collide head-on. The defensive player has a mass of 100 kg the offensive player has a mass of 90k (defense) (defense) (offense) __ What is the speed of the offensive player? square v What is the impulse of the offensive player? square v What is the impulse of the defensive player? square Looking at the last two answers, which of Newton's Laws does this best prove? square v

Here's how to solve this collision problem, assuming it's a perfectly inelastic collision (meaning they stick together after impact):<br /><br />**1. Conservation of Momentum:**<br /><br />The total momentum before the collision equals the total momentum after the collision. Momentum is calculated as mass * velocity (p=mv).<br /><br />* **Before Collision:**<br /> * Defensive player's momentum: 100 kg * 5 m/s = 500 kg⋅m/s<br /> * Offensive player's momentum: 90 kg * (-10 m/s) = -900 kg⋅m/s (negative because he's moving in the opposite direction)<br /> * Total momentum before: 500 kg⋅m/s + (-900 kg⋅m/s) = -400 kg⋅m/s<br /><br />* **After Collision:**<br /> * Combined mass: 100 kg + 90 kg = 190 kg<br /> * Combined velocity: Let's call this 'v'<br /> * Total momentum after: 190 kg * v<br /><br />* **Setting them equal:**<br /> * -400 kg⋅m/s = 190 kg * v<br /><br />* **Solving for v (combined velocity after collision):**<br /> * v = -400 kg⋅m/s / 190 kg <br /> * v ≈ -2.11 m/s (The negative sign indicates they are moving in the direction the offensive player was initially moving).<br /><br />**2. Impulse:**<br /><br />Impulse is the change in momentum.<br /><br />* **Offensive Player's Impulse:**<br /> * Final momentum (after collision): 90 kg * (-2.11 m/s) ≈ -189.9 kg⋅m/s<br /> * Initial momentum (before collision): -900 kg⋅m/s<br /> * Impulse = Final Momentum - Initial Momentum = -189.9 kg⋅m/s - (-900 kg⋅m/s) ≈ 710.1 kg⋅m/s<br /><br />* **Defensive Player's Impulse:**<br /> * Final momentum (after collision): 100 kg * (-2.11 m/s) ≈ -211 kg⋅m/s<br /> * Initial momentum (before collision): 500 kg⋅m/s<br /> * Impulse = Final Momentum - Initial Momentum = -211 kg⋅m/s - 500 kg⋅m/s ≈ -711 kg⋅m/s<br /><br />**3. Newton's Law:**<br /><br />The fact that the impulses are almost equal in magnitude but opposite in direction demonstrates **Newton's Third Law of Motion**: For every action, there is an equal and opposite reaction. The impulse one player experiences is equal and opposite to the impulse the other player experiences.<br /><br /><br />**Filled-in Blanks:**<br /><br />* What is the speed of the offensive player? **-2.11 m/s**<br />* What is the impulse of the offensive player? **710.1 kg⋅m/s**<br />* What is the impulse of the defensive player? **-711 kg⋅m/s**<br />* Looking at the last two answers, which of Newton's Laws does this best prove? **Newton's Third Law**<br />