Chapter 3 - Vectors and Coordinates Systems - Exercises and Problems - Page 79: 39

The component of Tom's weight that is parallel to the ladder is 566 N The component of Tom's weight that is perpendicular to the ladder is 376 N

Work Step by Step

We can find the angle $\theta$ that the ladder makes with the vertical. $cos(\theta) = \frac{2.5~m}{3.0~m}$ $\theta = arccos(\frac{2.5~m}{3.0~m})$ $\theta = 33.6^{\circ}$ We can find the component of Tom's weight $w$ that is parallel to the ladder. $w_{par}= w~cos(\theta)$ $w_{par}= (680~N)~cos(33.6^{\circ})$ $w_{par}= 566~N$ The component of Tom's weight that is parallel to the ladder is 566 N We can find the component of Tom's weight $w$ that is perpendicular to the ladder. $w_{perp} = w~sin(\theta)$ $w_{perp} = (680~N)~sin(33.6^{\circ})$ $w_{perp} = 376~N$ The component of Tom's weight that is perpendicular to the ladder is 376 N

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