Question

a piece of rope falls out of a hot air balloon from a height of 5,184 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 piece of rope to hit the ground? ? seconds

Explanation:

Step1: Set height to 0

When the rope hits the ground, $h(t)=0$. The initial height is 5184 ft, so the equation becomes $0=-16t^{2}+5184$.

Step2: Rearrange the equation

$16t^{2}=5184$.

Step3: Solve for $t^{2}$

$t^{2}=\frac{5184}{16}=324$.

Step4: Solve for $t$

$t = \sqrt{324}=18$ (we take the positive value since time cannot be negative).

Answer:

18