Answer:
18 seconds
Explanation:
Given the equation for height as a function of time expressed as
h(t) = -16t² - initial height, if initial height is 5,184ft, the expression will become;
h(t) = -16t² - 5,184
t is time in seconds
h(t) is height in feet
The height of the rope on the ground is zero. In order to calculate the amount of seconds it will take the piece of rope to hit the ground, we will substitute h(t) = 0 into the modeled equation as shown:
Since the body falls downwards (negative direction), initial height = -5184 ft
h(t) = -16t² - -(5,184)
0 = -16t² + 5,184
0+16t² = 5184
16t² = 5184
16t²/16 = 5184/16
t² = 324
t = √324
t = 18 seconds
Hence, it will take the rope 18seconds to hit the ground.