ection $2-20$ points each $($Work All Problems$)$

ABB gun uses a Hookean spring to fire a $BB$ by compressing its spring $4\mathrm{.}4$ cm $.$ The $BB$ gun is fired at a block of dense foam weighing $1$ kg suspended from a rope $5$ meters away. The BB gun is horizontal and parallel to the ground. The BB has a mass of $\mathrm{.}4$ g and lodges in the block when fired. When the BB strikes the block, it swings and rises $15$ cm above its initial level.

a$.$ How far should the target foam be lowered from the level of the gun for the BB to strike the center of the target?

b$.$ What is the spring constant of the spring used in the BB gun?

Skee$-$Ball is an old$-$style arcade game where solid, plastic balls are rolled up a ramp and fly as projectiles at a target ring as shown in the picture below $($somewhat simplified$).$ Skee$-$Balls are $7\mathrm{.}6$ cm in diameter and have a mass of $\mathrm{.}2$ kg $.$ If the ball lands perfectly in the cup, at what linear velocity must the ball leave the player's hand? Assume the ball is rolling the entire time on the ramp and that the ball leaves the ramp with an elevation of $40$ above horizontal. Friction is negligible.