Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 9 - Section 9.1 - Vectors in Two Dimensions - 9.1 Exercises - Page 639: 66

Answer

$25.1mi/h$, N $4.6^{\circ}$ W

Work Step by Step

Step 1. Identify the walking vector as $\vec {v_w} =-2i$ Step 2. Identify the liner moving vector as $\vec {v_l} =25j$ Step 3. The true vector of the total movement is the sum of the above two vectors: $\vec {v_t} =\vec {v_w} +\vec {v_l} =-2i+25j$ Step 4. The true speed is the modulus of the velocity: $|\vec {v_t} |=\sqrt {(-2)^2+(25)^2}\approx25.1mi/h$, and direction of the vector with respect to the $+x$-axis is $\theta=tan^{-1}\frac{25}{-2}\approx94.6^{\circ}$ or N $4.6^{\circ}$ W
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