Question

Kenny is standing on top of a boulder at his neighborhood pond. He picks up a small rock, so that it is 7 feet off the ground, and throws the rock into the pond. The height of the rock after seconds can be modeled by the expression −16t^2+32t+7.
Kenny wants to know the height of the rock at 1 second after it leaves his hand, t=1, and comes up with the answer 23 feet. How did Kenny find this result?

Answer 1

To find the height of the rock at \(t = 1\) second, Kenny would need to substitute \(t = 1\) into the height equation given:

\[
h(t) = -16t^2 + 32t + 7
\]

Now, substituting \(t = 1\):

\[
h(1) = -16(1)^2 + 32(1) + 7
\]

Calculating \(h(1)\):

1. Calculate \( (1)^2 \):
\[
(1)^2 = 1
\]

2. Substitute back in:
\[
h(1) = -16(1) + 32(1) + 7
\]

3. Now calculate:
\[
h(1) = -16 + 32 + 7
\]

4. Combine the values:
\[
-16 + 32 = 16
\]
\[
16 + 7 = 23
\]

Thus, \(h(1) = 23\) feet.

Kenny found the result of 23 feet by substituting \(t = 1\) into the height equation and performing the arithmetic as shown.