C$1989$A$13.$ A $2-$kilogram block is dropped from a height of $0\mathrm{.}45$ meter above an uncompressed spring as show above. The spring has an elastic constant of $200$ newtons per meter and negligible mass. The block strikes the end of the spring and sticks to it$.$Determine the speed of the block at the instant it hits the end of the spring.Determine the force in the spring when the block: reaches the equilibrium positionDetermine the distance that the spring is compressed at the equilibrium positionDetermine the speed of the block at the equilibrium positorIs the speed of the block a maxinum at the equilibrium position, explain