Monique is punting a football and the height of the ball travels is a function of time.

To find the height of the ball after 8.5 seconds, we need to evaluate the function \( h(s) = -s^2 + 10s + 3 \) at \( s = 8.5 \).

Let's plug in \( s = 8.5 \):

\[
h(8.5) = -(8.5)^2 + 10(8.5) + 3
\]

Calculating \( (8.5)^2 \):

\[
(8.5)^2 = 72.25
\]

Now substituting this value back into the equation:

\[
h(8.5) = -72.25 + 10 \times 8.5 + 3
\]

Calculating \( 10 \times 8.5 \):

\[
10 \times 8.5 = 85
\]

Now substitute this into the equation:

\[
h(8.5) = -72.25 + 85 + 3
\]

Now, combine the terms:

\[
h(8.5) = -72.25 + 85 + 3 = 85 - 72.25 + 3 = 12.75 + 3 = 15.75
\]

Thus, the height of the ball after 8.5 seconds is:

\[
\boxed{15.75}
\]