Problem $1.(25$ points$)$

Starting from rest when weight $L$ is on the ground, the gear $A,$ rotates clockwise with a constant angular acceleration of $5ra\frac{d}{s^2}.$

a$)$ Determine the time it takes for weight $L$ to lift $4$ feet off the ground.

b$)$ Calculate the velocity of the weight when it is $4$ feet off the ground.

c$)$ Calculate the angular velocity of gear B when the weight is $4$ feet off the ground.

As seen in the figure:

gear A has a diameter of $12$ inches

gear $B$ has a diameter of $36$ inches

gear C has a diameter of $48$ inches