The reason we set h equal to 0 is because h is height, and of course the height of an object when it is on the ground is 0. That looks like this then: [tex]0=-16t^2+1600[/tex]. To make this easier to factor, aka solving it for the time it takes to hit the ground, we will factor out a -16. That gives us this: [tex]0=-16(t^2-100)[/tex]. That means that, by the Zero Product Property, either -16=0, or [tex]t^2-100=0[/tex]. Of course [tex]-16 \neq 0[/tex], so that means that [tex]t^2-100=0[/tex]. We add 100 to both sides to get [tex]t^2=100[/tex]. Taking the square root of both sides, t = -10 and t = 10. The 2 things in math that will never EVER be negative are time and distance/length, so that means that -10 seconds is out. Therefore, t = 10 seconds.
