Question

If a ball is thrown into the air at 64 feet per second from the top of a 104​-foot-tall ​building, its height can be modeled by the function Sequals104plus64tminus16tsquared​, where S is in feet and t is in seconds. Complete parts a through c below.
height of ball three seconds after thrown

Answer 1

To find the height of the ball three seconds after it has been thrown, we can use the function given:

\[
S(t) = 104 + 64t - 16t^2
\]

We will substitute \( t = 3 \) seconds into the function:

\[
S(3) = 104 + 64(3) - 16(3^2)
\]

Calculating each term:

1. Calculate \( 64(3) \):
\[
64 \times 3 = 192
\]

2. Calculate \( 16(3^2) \):
\[
3^2 = 9 \quad \text{and then} \quad 16 \times 9 = 144
\]

Now substituting these values back into the equation:

\[
S(3) = 104 + 192 - 144
\]

Now, simplify:

\[
S(3) = 104 + 192 - 144 = 104 + 48 = 152
\]

So, the height of the ball three seconds after being thrown is **152 feet**.