**Problem Statement:**A ball, with a mass of 5 kg, accelerates in the \(+x\) direction with a magnitude of 5 m/s\(^2\) and in the \(-y\) direction with a magnitude of 2 m/s\(^2\). 1. What is the acceleration vector that describes this motion? 2. What is the net force on this ball?**Solution Explanation:**To find the acceleration vector, we combine the accelerations in the \(x\) and \(y\) directions:- The acceleration in the \(x\)-direction is \(+5 \, \text{m/s}^2\).- The acceleration in the \(y\)-direction is \(-2 \, \text{m/s}^2\).Thus, the acceleration vector \(\mathbf{a}\) is \(\mathbf{a} = (5 \, \text{m/s}^2) \, \mathbf{i} + (-2 \, \text{m/s}^2) \, \mathbf{j}\).To find the net force, we use Newton's second law, \(\mathbf{F} = m \mathbf{a}\), where \(m = 5 \, \text{kg}\).Substitute the given values:\[\mathbf{F} = 5 \, \text{kg} \cdot \left[(5 \, \text{m/s}^2) \, \mathbf{i} + (-2 \, \text{m/s}^2) \, \mathbf{j}\right]\]This results in:\[\mathbf{F} = (25 \, \text{N}) \, \mathbf{i} + (-10 \, \text{N}) \, \mathbf{j}\]Therefore, the net force on the ball is \(\mathbf{F} = 25 \, \text{N} \, \mathbf{i} - 10 \, \text{N} \, \mathbf{j}\).

A ball, with a mass of 5 kg, acceelerates in the +a direction with a magnitude of 5 m/s? and in the -y direction with a magnitude of 2 m/s2. What is the acceleration vector that describes this motion? What is the net force on this ball?

A ball, with a mass of 5 kg, acceelerates in the +a direction with a magnitude of 5 m/s? and in the -y direction with a magnitude of 2 m/s2. What is the acceleration vector that describes this motion? What is the net force on this ball?

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter3: Vectors

Section: Chapter Questions

Problem 13PQ: In Chapter 5, you will study a very important vector, force. Each case in Figure P3.13 shows an...

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