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…

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?

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?

Answer

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

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

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 $t\geq0$ (time cannot be negative in this context), $t=\sqrt{324}=18$.

Answer:

18