Answer
The acorn takes between 2 to 3 seconds to fall to the ground.
The graph for the function h(t)=100-16$t^{2}$ is shown below.
Work Step by Step
1. Graphically
Looking at the graph, when h=0, t=2.5 which shows that t=2.5 is the x-interectp on the graph. This also means that is takes 2.5 seconds for acorn to hit the ground as the height goes from 100ft at t=0secs to height 0ft at t=2.5
2. Mathematically,
The acorn when hits the ground has a height of 0 ft so we can make h(t)=0 and find the time.
0=100-16$t^{2}$
100=16$t^{2}$
$t^{2}$ = $\frac{100}{16}$
t=$\sqrt \frac{100}{16}$
t=2.5
Therefore, 2.5 is between 2 and 3 which are whole numbers.
