(Solved): As a part of an assembly process, the end effector at A on the robotic arm needs to move the gear ...

As a part of an assembly process, the end effector at $$A$$ on the robotic arm needs to move the gear at $$B$$ along the vertical line shown with some known velocity $$v_0$$ and acceleration $$a_0$$. Arm $$OA$$ can vary its length by telescoping via internal actuators, and a motor at $$O$$ allows it to pivot in the vertical plane. When $$?=50^{?}$$, it is required that $$v_0=8\mathrm{ft}/\mathrm{s}$$ (down) and that it slow down at $$a_0=2\mathrm{ft}/{\mathrm{s}}^2$$. Using $$h=4\mathrm{ft}$$, determine, at this instant, the values for $$\ddot{r}$$ (the extensional acceleration) and $$\ddot{?}$$ (the angular acceleration). (Round the final answers to four decimal places. Include minus sign if necessary.) The value of $$\ddot{r}$$ is $$\mathrm{ft}/{\mathrm{s}}^2$$. The value of $$\ddot{?}$$ is $$\mathrm{rad}/{\mathrm{s}}^2$$.