To find the height of the ball after 8.5 seconds, we can substitute \( s = 8.5 \) into the height function \( h(s) = -s^2 + 10s + 3 \).
Let's calculate \( h(8.5) \):
\[ h(8.5) = - (8.5)^2 + 10(8.5) + 3 \]
First, calculate \( (8.5)^2 \):
\[ (8.5)^2 = 72.25 \]
Next, calculate \( 10(8.5) \):
\[ 10(8.5) = 85 \]
Now, substitute these values back into the equation:
\[ h(8.5) = -72.25 + 85 + 3 \]
Now, add these values:
\[ h(8.5) = -72.25 + 85 + 3 = -72.25 + 88 \] \[ h(8.5) = 15.75 \]
Therefore, the height of the ball after 8.5 seconds is \( \boxed{15.75} \) meters.