Answer:
The object reaches the ground after 10 seconds.
Step-by-step explanation:
The height h (in feet) of the object after t seconds is modeled by the equation:
[tex]h=1600-16t^2[/tex]
And we want to determine the time at which the object reaches the ground.
If it reaches the ground, its height h above ground will be 0. So:
[tex]0=1600-16t^2[/tex]
We can solve for t. First, simplify by dividing both sides by 16:
[tex]0=100-t^2[/tex]
Factor using the difference of two squares pattern:
[tex]0=(10-t)(10+t)[/tex]
Zero Product Property:
[tex]10-t=0\text{ or } 10+t=0[/tex]
Solve for each case:
[tex]t=10\text{ or } t=-10[/tex]
Time cannot be negative. Thus, our only solution is:
[tex]t=10\text{ seconds}[/tex]
The object reaches the ground after 10 seconds.
