Question

Morgan throws a ball up in the air the height of the ball above the ground in feet is modeled by the function HT equals -16 T squared +2014 which he represents the time in seconds since the ball was thrown what is the appropriate domain for the situation

Answer 1

$H(T)=-16T^2+2014$

To find appropriate domain,put $H(T)\geqslant 0$ as the ball cannot go below the ground or the height cannot be negative and Time is always non negative that is $T\geqslant 0$ and,

$\implies -16T^2+2014\geqslant 0$

$\implies 2014 \geqslant 16 T^2$

$\implies \frac{2014}{16}=125.875 \geqslant T^2$

$\implies T\leqslant 11.21$ sec

or The domain will be $T \in [0,11.21]$ where $T$ is in seconds.