A ball is thrown from a rooftop with an initial downward velocity of magnitude v$0=4\mathrm{.}58$ m$/$s$.$ The rooftop is at height h$=17\mathrm{.}2$ meters above the ground. Use a coordinate system where upwards is positive.

Find the vertical component of the final velocity Vf$,$y$,$ in meters per second with which the ball hits the ground.

If we wanted the balls final speed to be exactly $27\mathrm{.}3$ m$/$s from what height in meters would we need to throw it with the same initial velocity

If the height is fixed at $17\mathrm{.}2$ m but we wanted the balls final speed to be $32\mathrm{.}7$ m$/$s what would the vertical component in meters per second of the intial velocity need to be$?$