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 t 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 after it leaves Kenny's hand, he can substitute \( t = 1 \) into the height equation provided. The height \( h(t) \) of the rock at time \( t \) seconds is given by the expression:

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

Now, we'll substitute \( t = 1 \) into the equation:

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

Calculating step-by-step:

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

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

3. Simplify the terms: \[ h(1) = -16 + 32 + 7 \]

4. Combine the values: \[ h(1) = 16 + 7 = 23 \]

Thus, the height of the rock at 1 second after it leaves his hand is indeed \( 23 \) feet. That's how Kenny arrived at the answer.