## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 6 - Section 6.7 - The Dot Product - Exercise Set - Page 793: 61

#### Answer

The work done is 22.05 foot-pounds.

#### Work Step by Step

Here, the force can be resolved into two vectors, such that: $\mathbf{F}=\left( 4\cos 50{}^\circ,4\sin 50{}^\circ \right)$ …… (1) As, the object is moved from point $\left( 3,7 \right)$ to $\left( 8,10 \right)$, therefore, the point to which the object has traveled is: \begin{align} & \mathbf{AB}=\left[ \left( 8,10 \right)-\left( 3,7 \right) \right] \\ & =\left[ \left( 8-3 \right),\left( 10-7 \right) \right] \\ & =\left( 5,3 \right) \end{align} $\mathbf{AB}=5\mathbf{i}+3\mathbf{j}$ …… (2) Now, as it is known that: $\mathbf{W}=\mathbf{F}\cdot \mathbf{AB}$ …… (3) Substituting equation (1) and (2) in equation (3), \begin{align} & \mathbf{W}=\left( 4\cos 50{}^\circ,4\sin 50{}^\circ \right)\cdot \left( 5,3 \right) \\ & =\left[ \left( 4\cos 50{}^\circ \times 5 \right)+\left( 4\sin 50{}^\circ \times 3 \right) \right] \\ & =20\cos 50{}^\circ +12\sin 50{}^\circ \\ & \approx 22.05 \end{align}

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