For problem $2,$ use the position function $p(t)=-16t^{2}50t{p}_0,$ where $p$ is measured in fee $t$ in seconds and to and $p_0$ are the initial velocity and position respectively.

$2.$ A professional baseball pitcher was capable of throwing a baseball $160f\frac{t}{s}.$ During his caree he had the opportunity to pitch in the Houston Astrodome. The Astrodome was an indod stadium with a ceiling $208$ feet high.

$($a$)$ Could the pitcher have hit the ceiling of the Astrodome if he were capable of giving baseball an upward velocity of $100f\frac{t}{s}$ from a height of $7\mathrm{.}5$ ft $?$

$($b$)$ How fast would the pitcher have to throw a ball upward from a height of $7\mathrm{.}5$ feet in orde to hit the ceiling of the Astrodome?