Solved: At the instant shown, the backhoe is traveling

Chapter 20, Problem 20-49

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At the instant shown, the backhoe is traveling forward at a constant speed \(v_{O}=2 \ \mathrm{ft} / \mathrm{s}\), and the boom ABC is rotating about the z axis with an angular velocity \(\omega_{1}=0.8 \ \mathrm{rad} / \mathrm{s}\) and an angular acceleration \(\dot{\omega}_{1}=1.30 \ \mathrm{rad} / \mathrm{s}^{2}\). At this same instant the boom is rotating with \(\omega_{2}=3 \ \mathrm{rad} / \mathrm{s}\) when \(\dot{\omega}_{2}=2 \ \mathrm{rad} / \mathrm{s}^{2}\), both measured relative to the frame. Determine the velocity and acceleration of point P on the bucket at this instant.