To find the height of the ball after 7.5 seconds, we need to evaluate the function \( h(s) = -s^2 + 10s + 3 \) at \( s = 7.5 \).
Plugging in \( s = 7.5 \):
\[ h(7.5) = -(7.5)^2 + 10(7.5) + 3 \]
Calculating each term:
- \( (7.5)^2 = 56.25 \)
- \( 10(7.5) = 75 \)
Now substitute these values back into the equation:
\[ h(7.5) = -56.25 + 75 + 3 \]
Adding these values together:
\[ h(7.5) = -56.25 + 75 = 18.75 \]
Next, add 3:
\[ h(7.5) = 18.75 + 3 = 21.75 \]
So, the height of the ball after 7.5 seconds is \( \boxed{21.75} \).