**Problem Statement:**Two balls with masses \( m_1 = 2 \, \text{kg} \) and \( m_2 = 4 \, \text{kg} \) are moving with velocities of \[\vec{v_1} = (5\hat{i} - 3\hat{j} + 8\hat{k}) \, \text{m/s} \]and \[\vec{v_2} = (1\hat{i} + 5\hat{j} - 12\hat{k}) \, \text{m/s} \]when they collide and stick together. What is:- The velocity of the balls after the collision.- The type of collision described.**Solution:**1. **Velocity After Collision:** - When two objects stick together after a collision, it is an inelastic collision. The combined velocity can be found using the conservation of momentum: \[ m_1\vec{v_1} + m_2\vec{v_2} = (m_1 + m_2)\vec{v_f} \] - Solve for \(\vec{v_f}\): \[ \vec{v_f} = \frac{m_1\vec{v_1} + m_2\vec{v_2}}{m_1 + m_2} \] - Calculate: \[ \vec{v_f} = \frac{2(5\hat{i} - 3\hat{j} + 8\hat{k}) + 4(1\hat{i} + 5\hat{j} - 12\hat{k})}{2 + 4} = \frac{(10\hat{i} - 6\hat{j} + 16\hat{k}) + (4\hat{i} + 20\hat{j} - 48\hat{k})}{6} \] \[ = \frac{(14\hat{i} + 14\hat{j} - 32\hat{k})}{6} = \left(\frac{14}{6}\hat{i} + \frac{14}{6}\hat{j} - \frac{32}{6}\hat{k}\right)

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Two balls with masses m1 = 2kg and m2 = 4kg are moving with velocities of v1 = (5i – 3j+8k) m/s and v2 = (li +5j – 12k) m/s when they collide and stick together. What is: • The velocity of the balls after the collisions. • The type of collision described.

Two balls with masses m1 = 2kg and m2 = 4kg are moving with velocities of v1 = (5i – 3j+8k) m/s and v2 = (li +5j – 12k) m/s when they collide and stick together. What is: • The velocity of the balls after the collisions. • The type of collision described.

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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