### Problem Statement:A projectile (mass = 0.227 kg) is fired and embeds itself in a target (mass = 1.88 kg). (The target is initially stationary). The target (with the projectile in it) flies off after being struck. What percentage of the projectile's incident kinetic energy does the target (with the projectile in it) carry off after being struck?### Explanation and Solution:To solve this problem, we will use the principles of conservation of momentum and kinetic energy.#### Step 1: Conservation of MomentumThe initial momentum of the system is the momentum of the projectile, as the target is stationary. The final momentum is the combined momentum of the target and the projectile after the collision.Let's denote:- Mass of the projectile as \( m_p = 0.227 \) kg- Mass of the target as \( m_t = 1.88 \) kg- Initial velocity of the projectile as \( v_p \)- Final combined velocity of the target and projectile as \( v_f \)Using the conservation of momentum:\[ m_p \cdot v_p = (m_p + m_t) \cdot v_f \]From this, we can solve for \( v_f \):\[ v_f = \frac{m_p \cdot v_p}{m_p + m_t} \]#### Step 2: Initial Kinetic Energy of the ProjectileThe initial kinetic energy (\( KE_{initial} \)) of the projectile is given by:\[ KE_{initial} = \frac{1}{2} m_p v_p^2 \]#### Step 3: Final Kinetic Energy of the Combined SystemThe final kinetic energy (\( KE_{final} \)) of the combined system is:\[ KE_{final} = \frac{1}{2} (m_p + m_t) v_f^2 \]Substituting \( v_f \):\[ KE_{final} = \frac{1}{2} (m_p + m_t) \left( \frac{m_p \cdot v_p}{m_p + m_t} \right)^2 \]\[ KE_{final} = \frac{1}{2} \frac{m_p^2 \cdot v_p^2}{m_p + m_t} \]#### Step 4: Percentage of Kinetic Energy Carried OffTo find the percentage of the projectile's

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Description: ### Problem Statement:A projectile (mass = 0.227 kg) is fired and embeds itself in a target (mass = 1.88 kg). (The target is initially stationary). The target (with the projectile in it) flies off after being struck. What percentage of the projectil

Given data*The mass of the projectile is m = 0.227 kg*The mass of the stationary target is M = 1.88…

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A projectile (mass = 0.227 kg) is fired at and embeds itself in a target (mass = 1.88 kg). (The target is initially stationary). The target (with the projectile in it) flies off after being struck. What percentage of the projectile's incident kinetic energy does the target (with the projectile in it) carry off after being struck?

A projectile (mass = 0.227 kg) is fired at and embeds itself in a target (mass = 1.88 kg). (The target is initially stationary). The target (with the projectile in it) flies off after being struck. What percentage of the projectile's incident kinetic energy does the target (with the projectile in it) carry off after being struck?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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