A projectile is shot horizontally at $13\mathrm{.}4$ m$/$s from the roof of a building $65\mathrm{.}0$ m tall.

$($a$)$ Determine the time necessary for the projectile to reach the ground below.

$($b$)$ Determine the distance from the base of the building that the projectile lands.

$($c$)$ Determine the horizontal and vertical components of the velocity just before the projectile reaches the ground.