Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 6 - Section 6.6 - Vectors - Exercise Set - Page 783: 75


The force required to pull the box is 30.9 pounds.

Work Step by Step

${{\mathbf{F}}_{1}}=-100\mathbf{j}$ Find the length of BC as below: $\begin{align} & {{\mathbf{F}}_{\mathbf{2}}}=95\cos 288{}^\circ \mathbf{i}+95\sin 288{}^\circ \mathbf{j} \\ & =29.41\mathbf{i}-90.4\mathbf{j} \end{align}$ The resulting vector will be obtained as below: $\begin{align} & \mathbf{F}={{\mathbf{F}}_{1}}-{{\mathbf{F}}_{\mathbf{2}}} \\ & =\left( -100\mathbf{j} \right)-\left( 29.4\mathbf{i}-90.4\mathbf{j} \right) \\ & =-29.4\mathbf{i}-9.6\mathbf{j} \end{align}$ So, the magnitude of force vector is given by $\begin{align} & \left| \left| \mathbf{F} \right| \right|=\sqrt{{{\left( -29.4 \right)}^{2}}+{{\left( -9.6 \right)}^{2}}} \\ & \approx 30.9 \end{align}$
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