Answer:
0.375 second and 3.5 second
Step-by-step explanation:
The position can be modeled by a quadratic function [tex]\displaystyle{h=-16t^2+62t+6}[/tex]. We are tasked to find the time when a ball reaches a height of 27 feet. Therefore, let h = 27:
[tex]\displaystyle{27=-16t^2+62t+6}[/tex]
Solve for t:
[tex]\displaystyle{27-6=-16t^2+62t}\\\\\displaystyle{21=-16t^2+62t}\\\\\displaystyle{16t^2-62t+21=0}[/tex]
Since the equation is quite complicated and more time-consuming to solve, i'll skip the factoring or quadratic part:
[tex]\displaystyle{t=0.375, 3.5}[/tex]
After done solving the equation, you'll get t = 0.375 and 3.5 seconds. These solutions are valid since both are positive values and time can only be positive.
Hence, it'll take 0.375 and 3.5 seconds for a ball to reach 27 feet.
