$(8)$ In physics class students launch a projectile horizontally off a roof that is $50\mathrm{.}0$ m above the level ground below. They intend to hit a target on a level area below, $256$ m from the base of the building. Use $g=9\mathrm{.}80\frac{m}{s^2}$ and ignore air resistance.

a$.(4)$ How long will the projectile fly until it hits the ground?

b$.(4)$ What initial horizontal velocity, $v_{i,x}$ is needed so that the projectile hits the target?