## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 6 - Section 6.7 - The Dot Product - Exercise Set - Page 793: 57

#### Answer

The work done is 1079 foot-pounds.

#### Work Step by Step

Here, the box is pulled horizontally, such that the angle between the force and direction of motion is $\left( 38{}^\circ -12{}^\circ \right)$. Now it is known, $\mathbf{W}=\left\| \mathbf{F} \right\|\left\| \mathbf{AB} \right\|\cos \theta$ …… (1) As it is given that, $\left\| \mathbf{F} \right\|=60,\left\| \mathbf{AB} \right\|=20$ and $\theta =\left( 38-12 \right){}^\circ$ …… (2) Therefore, use (2) in (1). So, \begin{align} & \mathbf{W}=\left( 60 \right)\left( 20 \right)\cos \left( 38-12 \right){}^\circ \\ & =\left( 1200 \right)\cos \left( 26{}^\circ \right) \\ & =\left( 1200 \right)\left( 0.898 \right) \\ & \approx 1079 \end{align}

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