a pebble falls off of a cliff at a height of ...
a pebble falls off of a cliff at a height of 2,304 ft. if the equation for height as a function of time is h(t) = -16t² + initial height where t is time in seconds and h(t) is height in feet, how many seconds will it take for the pebble to hit the ground? ? seconds
Answer
# Explanation:
## Step1: Set height to 0
When the pebble hits the ground, $h(t)=0$. The initial - height is 2304 ft, so the equation becomes $0=-16t^{2}+2304$.
## Step2: Rearrange the equation
Add $16t^{2}$ to both sides of the equation: $16t^{2}=2304$.
## Step3: Solve for $t^{2}$
Divide both sides by 16: $t^{2}=\frac{2304}{16}=144$.
## Step4: Solve for $t$
Take the square - root of both sides. Since $t$ represents time and cannot be negative in this context, $t = \sqrt{144}=12$.
# Answer:
12