Fundamentals of Physics Extended (10th Edition)

Published by Wiley
ISBN 10: 1-11823-072-8
ISBN 13: 978-1-11823-072-5

Chapter 4 - Motion in Two and Three Dimensions - Problems: 8b

Answer

-$63.4^{\circ}$ from the positive x axis or 63.4 degrees South of due East

Work Step by Step

(Look at Picture for help) The plane starts at the point (0,0) and it ends at the point (483, -966). We can connect these two points with a line and then we can define the direction of displacement as the angle that this line makes with the positive x axis (angle labeled as $\theta$ To find the value of theta, we can use trigonometry. We know that the side opposite theta is 966km (y coordinate of point) and that the side adjacent to theta is 483km (x coordinate of point). Therefore we know that $ tan(\theta) = \frac{966}{483} $ so then $\theta = 63.4^{\circ} $ However, this angle is negative since the positive direction is defined as counterclockwise around the positive x axis
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