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.

Question

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.