Problem # $4(12$ Marks$)$:

The winch is used to raise the load w $($mass $=60kg)$ as shown in the figure below with mass of all pulley are negligible. Determine the following:

a$)$ If the speed of the load $w$ is $1\mathrm{.}2\frac{m}{s}$ up$,$ what is speed of cable that is drawn in by the motor?

b$)$ If the acceleration of cable that is drawn in by the motor is $2\mathrm{.}4\frac{m}{s^2},$ what is the tension in the cable drawn by the motor?

c$)$ What is the input electrical power to the motor if motor efficiency is $0\mathrm{.}81?$

In order to solve this problem, use the figure below to draw the references and position coordinate axes needed to describe motion.