Answer
$t=1$ second
Tick marks: $0.25, 0.50, 0.75, 1, 1.25$
Work Step by Step
The gymnast will reach the ground when $s(t)=0$. We solve the equation for $t$:
$$\begin{align*}
-16t^2+8t+8&=0\quad&&\text{Write the given equation.}\\
2t^2-t-1&=0\quad&&\text{Divide each term by }-8.\\
(t-1)(2t+1)&=0\quad&&\text{Factor.}\\
t-1=0&\text{ or }2t+1=0\quad&&\text{Set each factor equal to }0.\\
t=1&\text{ or }t=-0.5\quad&&\text{Solve the resulting equations.}
\end{align*}$$
The equation has two solutions: $t=1$ and $t=-0.5$. Because $t$ must be positive as it represents time, the only solution is $t=1$. This means that the gymnast reaches the ground in one second.
Each tick mark along the horizontal axis is drawn each $1/4=0.25$ seconds: $0.25, 0.50, 0.75, 1, 1.25$.
