Problem Statement: Cylindrical Robotic Arm Intercepting a Moving Package

A cylindrical robotic arm is tasked with intercepting packages moving along a conveyor belt, and dropping them in a bin. The package on the conveyor belt is located at point P $(3,-3)$ and the bin, point B at $(-2,0).$

The conveyor belt moves at a constant speed of $20$ meters per minute$*.$ The robotic arm operates in a horizontal plane and rotates with a controllable acceleration counterclockwise about its fixed axle. The arm consists of a single extending segment with a maximum extension length of $4$m$,$ which extends and retracts at a controllable speed. The robot is initially stationary facing $180$ deg away from the conveyor belt along the x axis with the grip$($Point G$)$ at $(-2,0)$

Assumptions:

The robot begins rotating and extending simultaneously as the package starts moving.

Deliverables:

$1.$ The y$-$coordinate of the package at the time of interception.

$2.$ The speed of arm extension $($v ext$)$ required for interception.

$3.$ The angular acceleration $($$)$ required for interception$$