A baseball pitcher throws a fastball horizontally at a speed of $42\mathrm{.}0$ m$/$s from the pitcher's mound to home plate, which is $60$ feet, $6$ inches away.

A$)$ How long does it take the ball to reach home plate?

B$)$ How fast is the ball dropping $($y$-$component of velocity$)$ when it crosses home plate?

C$)$ What is the velocity of the ball when it crosses home plate?

D$)$ How far has the ball dropped when it crosses home plate?