Answer:
6 seconds.
Step-by-step explanation:
We have been given a function formula [tex]f(t)=-5t^2+20t+60[/tex] that models the approximate height of an object t seconds after it is launched.
To find the number of seconds it will take the object to hit the ground, we need to find the zeros of our given function.
[tex]-5t^2+20t+60=0[/tex]
Upon dividing our equation by -5 we will get,
[tex]t^2-4t-12=0[/tex]
We will factor our given equation by splitting the middle term as:
[tex]t^2-6t+2t-12=0[/tex]
[tex]t(t-6)+2(t-6)=0[/tex]
[tex](t-6)(t+2)=0[/tex]
[tex](t-6)=0\text{ or }(t+2)=0[/tex]
[tex]t=6\text{ or }t=-2[/tex]
Since time cannot be negative, therefore, it will take the object 6 seconds to hit the ground.