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 up the equation

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

Add $16t^{2}$ to both sides: $16t^{2}=5184$.

Step3: Solve for $t^{2}$

Divide both sides by $16$: $t^{2}=\frac{5184}{16}=324$.

Step4: Solve for $t$

Take the square - root of both sides. Since $t$ represents time and cannot be negative, we have $t = \sqrt{324}=18$.

Answer:

18