University Physics with Modern Physics (14th Edition)

Published by Pearson
ISBN 10: 0321973615
ISBN 13: 978-0-32197-361-0

Chapter 3 - Motion in Two or Three Dimensions - Problems - Exercises - Page 93: 3.1

Answer

(a) $v_{av,x} = 1.4~m/s$ $v_{av,y} = -1.3~m/s$ (b) $v_{av} = 1.9~m/s$ The angle below the positive x-axis is $42.9^{\circ}$

Work Step by Step

At $t_1 = 0$, the coordinates of the squirrel are $(1.1~m, 3.4~m)$. At $t_2 = 3.0~s$, the coordinates of the squirrel are $(5.3~m, -0.5~m)$. (a) $v_{av,x} = \frac{\Delta x}{\Delta t} = \frac{5.3~m-1.1~m}{3.0~s} = 1.4~m/s$ $v_{av,y} = \frac{\Delta y}{\Delta t} = \frac{-0.5~m-3.4~m}{3.0~s} = -1.3~m/s$ (b) We can find the magnitude of the average velocity $v_{av}$. $v_{av} = \sqrt{(v_{av,x})^2+(v_{av,y})^2}$ $v_{av} = \sqrt{(1.4~m/s)^2+(-1.3~m/s)^2}$ $v_{av} = 1.9~m/s$ We can find the angle below the positive x-axis. $tan(\theta) = \frac{1.3}{1.4}$ $\theta = tan^{-1}(\frac{1.3}{1.4}) = 42.9^{\circ}$
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