## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 6 - Section 6.7 - The Dot Product - Exercise Set - Page 793: 58

#### Answer

The work done is 1841 foot-pounds.

#### Work Step by Step

Here, the box is pulled horizontally, such that the angle between the force and direction of motion is $\left( 33{}^\circ -10{}^\circ \right)$. Now it is known, $\mathbf{W}=\left\| \mathbf{F} \right\|\left\| \mathbf{AB} \right\|\cos \theta$ …… (1) As it is given that, $\left\| \mathbf{F} \right\|=80,\left\| \mathbf{AB} \right\|=25$ and $\theta =\left( 33-10 \right){}^\circ$ …… (2) Therefore, using (2) in (1) \begin{align} & \mathbf{W}=\left( 80 \right)\left( 25 \right)\cos \left( 33-10 \right){}^\circ \\ & =\left( 2000 \right)\cos \left( 23{}^\circ \right) \\ & =\left( 2000 \right)\left( 0.920 \right) \\ & \approx 1841 \end{align}

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