Question $5(24$ Marks Total$)$

The uniform crate, illustrated in Figure Q$5,$ has mass $900$ kg $.$ The crate is suspended by two light cables of fixed length at $\backslash ($ A $\backslash )$ and $\backslash ($ B $\backslash )$ and held by a light rope at $\backslash ($ C $\backslash ),$ such that the angle $\backslash (\backslash$theta$=45^\{\backslash$circ$\}\backslash ).$ The rope $\backslash ($ C $\backslash )$ is suddenly released, allowing the crate to swing freely, supported by the cables at $\backslash ($ A $\backslash )$ and $\backslash ($ B $\backslash ).$

$($a$)$ Determine the acceleration of the centre of mass of the crate just after release. Give the result in $\backslash (\backslash$mathrm$\{$m$\}/\backslash$mathrm$\{$s$\}^\{2\}\backslash )$ to three or four significant figures.

$($b$)$ Determine the tension in each of the cables just after release. Give the result in kN to three or four significant figures.