The height \( H \) of a projectile launched from ground level is a function of the time \( t \) it is in the air. The height in feet for \( t \) seconds is given by the function \( H(t)=-16 t^{2}+96 t \). What is the domain of the function? (Enter your answer using interval notation.) What does the domain mean in the context of the problem? After the projectile is launched from ground level it takes ground.

The domain of the function \( H(t) = -16 t^{2} + 96 t \) is \([0, 6]\). This interval means that the time \( t \), measured in seconds, is restricted to values starting from 0 (the moment of launch) to 6 seconds (when the projectile hits the ground again). In the context of the problem, the domain represents the time duration during which the projectile is in the air. Before \( t=0 \), the projectile hasn’t been launched, and after \( t=6 \), it has already hit the ground, thus no longer rising or falling.