The hydraulic cylinder produces a limited horizontal motion of point \(A\). If \(v_{A}=4 \mathrm{~m} / \mathrm{s}\) when \(\theta=45^{\circ}\), determine the magnitude of the velocity of \(D\) and the angular velocity \(\omega\) of \(A B D\) for this position.

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A VA 400 200 mm mm B 250 mm D