Answered: An object moves 8.0 m at an angle of…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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An object moves 8.0 m at an angle of 20.0^o with respect to its x-axis. The object then moves another 10.0 m at an angle of 40.0^o with respect to its current position. Analytically determine the magnitude and direction of the displacement of this object

Expert Solution

Net displacement vector

$\begin{array}{rcl} {\overset{⇀}{d}}_{n e t} & = & [(8.0 m) (\cos 20.0 °) \hat{i} + (8.0 m) (\sin 20.0 °) \hat{j}] + [(10.0 m) (\cos 40.0 °) \hat{i} + (10.0 m) (\sin 40.0 °) \hat{j}] \\ = & (15.2 m) \hat{i} + (9.16 m) \hat{j} \end{array}$

Magnitude of net displacement.

$\begin{array}{rcl} d & = & \sqrt{x^{2} + y^{2}} \\ = & \sqrt{{(15.2 m)}^{2} + {(9.16 m)}^{2}} \\ = & 17.7 m \end{array}$

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