To find the height of the ball after 7.5 seconds, we need to evaluate the function \( h(s) = -s^2 + 10s + 3 \) at \( s = 7.5 \).
Start by substituting \( s = 7.5 \) into the function:
\[
h(7.5) = - (7.5)^2 + 10(7.5) + 3
\]
Now calculate each term:
1. \( (7.5)^2 = 56.25 \)
2. \( 10 \times 7.5 = 75 \)
Now substitute these values into the equation:
\[
h(7.5) = -56.25 + 75 + 3
\]
Now calculate it step by step:
1. \( -56.25 + 75 = 18.75 \)
2. \( 18.75 + 3 = 21.75 \)
Thus, the height of the ball after 7.5 seconds is
\[
\boxed{21.75}
\]