Problem H$\mathrm{.}1.$I

Given: An inextensible cable $(1)$ is attached to fixed ground at end D and to the center of pulley C at the other end, with the cable wrapped around a pulley that is mounted on block A $.$ A second inextensible cable $(2)$ is attached to fixed ground at end D and to block B $,$ with the cable being wrapped around pulley C$.$ Block A is known to have a speed and acceleration of $v_A$ and $a_A,$ respectively, up the incline on which A and B move.

Find: For this problem:

$($a$)$ Determine the speed of B

$($b$)$ Determine the magnitude of the acceleration of B$.$

Use the following parameters in your analysis: $v_A=10\frac{m}{s},a_A=4\frac{m}{s^2}$ and $=24.$