(Solved): For the device shown below, collars \( A \) and \( C \) are pinned together at point \( C \), and ...

For the device shown below, collars \( A \) and \( C \) are pinned together at point \( C \), and they slide on rods \( B \) and \( S \), respectively. \( \operatorname{Rod} B \) has a constant angular velocity \( \dot{\theta} \hat{k} \) for \( 10^{\circ} \leq \theta \leq 45^{\circ} \). Find the relative velocity of point \( C \) with respect to rod \( B \), as a function of \( D, \theta, \dot{\theta} \) in this range of angles. \[ \begin{array}{l} \vec{\nu}_{R E L}=\frac{D \dot{\theta} \tan \theta}{\cos \theta}(\cos \theta \hat{i}+\sin \theta \hat{j}) \\ \vec{\nu}_{R E L}=\frac{D \dot{\theta} \tan \theta}{\cos \theta}(\sin \theta \hat{i}+\cos \theta \hat{j}) \\ \vec{\nu}_{R E L}=\frac{D \dot{\theta} \tan \theta}{\sin \theta}(\cos \theta \hat{i}+\sin \theta \hat{j}) \end{array} \] None of the above