Question

If an apple is launched out of a fruit cannon vertically upward from ground level with an initial velocity of 80 feet per second, then its height h after t seconds is given by the equations h(t)= -16t²+80t (if air resistance is neglected). How long will it take for the apple to return to the ground?

Answer 1

"Return to the ground at a time $t_0$ " is the same as $h(t_0)=0$, so we have to find roots of $h(t)$.

$h(t)=-16t^2+80t=-16t(t-5)$, so the roots are $t_0=5, t_0'=0$. But the second root has an obvious meaning, at the time 0 the apple was on the ground. Therefore the "correct" root to choose is $t_0=5s$