**Problem Statement:**Two piloted satellites approach one another at a relative speed of 0.250 m/s, intending to dock. The first satellite has a mass of \(4.00 \times 10^3 \, \text{kg}\), and the second satellite has a mass of \(7.50 \times 10^3 \, \text{kg}\). If the two satellites collide elastically rather than dock, what is their final relative velocity?**Explanation:**This problem involves applying the principles of elastic collisions to calculate the final relative velocity of two colliding bodies. Elastic collisions are those in which both momentum and kinetic energy are conserved. To solve, we need to use:1. Conservation of Momentum: \[ m_1 \cdot v_{1i} + m_2 \cdot v_{2i} = m_1 \cdot v_{1f} + m_2 \cdot v_{2f} \] where \(m_1\) and \(m_2\) are the masses, \(v_{1i}\) and \(v_{2i}\) are the initial velocities, and \(v_{1f}\) and \(v_{2f}\) are the final velocities.2. Conservation of Kinetic Energy: \[ \frac{1}{2}m_1 \cdot (v_{1i})^2 + \frac{1}{2}m_2 \cdot (v_{2i})^2 = \frac{1}{2}m_1 \cdot (v_{1f})^2 + \frac{1}{2}m_2 \cdot (v_{2f})^2 \]Given initial velocities based on the relative speed, solve these equations simultaneously to find the final velocities and then determine the relative velocity.

Two piloted satellites approach one another at a relative speed of 0.250 m/s, intending to dock. The first has a mass of 4.00×10³kg, and the second a mass of 7.50×10³kg. If the two satellites collide elastically rather than dock, what is their final relative velocity?

Two piloted satellites approach one another at a relative speed of 0.250 m/s, intending to dock. The first has a mass of 4.00×10³kg, and the second a mass of 7.50×10³kg. If the two satellites collide elastically rather than dock, what is their final relative velocity?

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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