Question $7(10$ Marks, CLO: $3,4)$Dynamic$)$

The free$-$rolling ramp has a mass of $30$ kg $.$

The $10$ kg crate slides from rest at $\backslash (\backslash$mathrm$\{$A$\},3\mathrm{.}5\backslash$mathrm$\{$~m$\}\backslash )$ down the ramp to $\backslash ($ B $\backslash ).$

Assume that the ramp is smooth and neglect the mass of the wheels.

Part $1.$ Determine the ramp's speed when the crate reaches $\backslash ($ B $\backslash ).$

Part $2.$ Determine the ramp's acceleration when the crate reaches B$.$