Halliday, Resnick & Walker — Vectors: Problem 51

Rock faults are ruptures along which opposite faces of rock have slid past each other. In Fig. 3.15, points A and B coincided before the rock in the foreground slid down to the right. The net displacement $\vec{AB}$ is along the plane of the fault. The horizontal component of $\vec{AB}$ is the strike-slip AC. The component of $\vec{AB}$ that is directed down the plane of the fault is the dip-slip AD. (a) What is the magnitude of the net displacement $\vec{AB}$ if the strike-slip is 22.0 m and the dip-slip is 17.0 m? (b) If the plane of the fault is inclined at angle $\phi = 52.0^\circ$ to the horizontal, what is the vertical component of $\vec{AB}$?