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To find the height of the ball after 7.5 seconds using the function \( h(s) = -s^2 + 10s + 3 \), we need to substitute \( s = 7.5 \) into the equation.
Let's calculate \( h(7.5) \):
\[
h(7.5) = - (7.5)^2 + 10(7.5) + 3
\]
Calculating \( (7.5)^2 \):
\[
(7.5)^2 = 56.25
\]
Now substituting this back into the equation:
\[
h(7.5) = -56.25 + 75 + 3
\]
Now, calculating:
\[
h(7.5) = -56.25 + 75 + 3 = -56.25 + 78 = 21.75
\]
Thus, the height of the ball after 7.5 seconds is:
\[
\boxed{21.75}
\]