$1.$ A$=70$ mass is launched from rest by a $=2$ compressed spring of stiffness $=630.$ The mass $$ moves across the horizontal surface and then down the $25$ tall hill and is launched from end of the $3$ tall ramp on the right inclined at $=300$ measured with respect to the horizontal. All surfaces the mass moves on are frictionless.

$($a$)$ Using the work$-$kinetic energy theorem, what is the speed of the mass at point A$,$ just before the mass goes down the hill?

$($b$)$ Using energy ideas between points A and B$,$ what is the launch speed of the mass from the end of the ramp?

$($c$)$ The mass eventually lands at point C$.$ How far horizontally is point C from point B$?$

$($d$)$ How much work was done by gravity between points B and C$?$