Consider the track shown in Figure $3.$ A block of mass $3\mathrm{.}0$ kg is released from rest at point A $.$ Section $AB$ of the track is frictionless. Section $BC$ is rough and the coefficient of kinetic friction between the surfaces is ${}_k=0\mathrm{.}50.$ Section CD is frictionless. The spring constant is $600\frac{N}{m}.$

$($a$)$ Determine the speed of the block at point C $($just before it hits the spring$).$

$($b$)$ How far does the block compress the spring?

$($C$)$ What vertical distance does it move up the plane?

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