Question

h(s)=-s^2 +10s+3. After flying through the air for 8.5 seconds what is the height of the ball

Answer 1

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.