Consider the two$-$link planar manipulator with lengths $L_1=2m$ and $L_2=3m.$

$($a$)$ Using its Jacobian, calculate the end$-$effector linear velocity if joint $1$ is rotating at $1ra\frac{d}{s}$ and joint $2$ is rotating at $3ra\frac{d}{s}$ for ${}_1=167\mathrm{.}028$ and ${}_2=-{156\mathrm{.}44}^0.$

$($b$)$ Calculate the resulting joint torque $,$ given a force $F=(30,-20)$ is applied to the end$-$effector.