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