In this project, you are required to provide the solution$($s$)$ that can lift the mass A up to the top of the inclined plane as shown in the diagram below. Given that the mass B is $2$ kg $,$ the length L is $3$ m $,$ and the inclined angle is $\backslash (30^\{\backslash$circ$\}\backslash ).$ Different scenarios are given as follows:

$(*$Note: small offsets, such as the distance between the pulley and the wall$/$ceiling$,$ the size of the mass and the pulley can be neglected. The friction between the mass and the plane can be neglected.$).$

Scenario $1$: Find the mass A of the system

$($a$)$ Set up the system equation for mass B

$($b$)$ Set up the system equation for mass A

$($c$)$ Find the distance travelled by mass A $($y$)$ when mass B reaches the ground floor

$($d$)$ Knowing that the distance travelled in x and y $,$ find the maximum mass A that can be lifted $($Hint: the acceleration must be $??)$