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: 2c


122 degrees

Work Step by Step

Looking at the picture provided, the watermelon seed lies at the point (-5,8), which is shown in black. Therefore, the position vector is the vector from (0,0) to the point (-5,8). The angle that this vector makes with the x axis (shown in red as $ \theta$) is the angle we are looking for. To find this angle, we can use basic trigonometry. We know that the length of the side opposite the angle is 8m (since y = 8m) and that the length of the side adjacent is 5m (since x = -5m). We use the formula $ tan\theta = opposite/adjacent = 8/5$ Solving for $\theta$, we see that it equals 57.99 degrees. However, the angle shown in the picture is the angle the vector makes with the NEGATIVE direction of the x axis, not the positive direction. In order to find the angle it makes with the positive, we need to find the complementary angle to $\theta$ (90-$\theta$ = 32). However, this will give us the angle from the vector to the positive y axis. In order to find the angle between the vector and the positive x axis, we need to add another 90 degrees (the separation between the x and y axis). We then get that the angle = 90 + 32 = 122 degrees
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