A solid block of weight $200$ N rests on a rough horizontal surface with tractive resistance $(Tr=32N),$ as shown in figure below. The block is pulled by a force of $80$ N applied at an angle $30$ to the horizontal. Determine:

$($a$)$ Velocity of block $($in $\frac{m}{s})$ after it has moved $20$ m starting from rest.

$($b$)$ Calculate the further distance moved by block $($in m $)$ if the pulley is removed.