A child that drops a rock off a building that is 64 feet tall. If the equation for height as a function of time is h(t)=-16t2+ initial height where t is time in seconds and h(t) is height in feet, how many seconds will it take for the rock to hit the ground?

The equation for free fall (as opposed to parabolic motion which would occur if the child threw the rock up into the air and it followed a parabolic path. This equation would have an upwards velocity value in it. Dropping something does not have an upwards velocity value because we are not throwing it up into the air and letting gravity take over. VERY important distinction when working with these problems!):

[tex]h(t)=-16t^2+64[/tex] and we need to know how long it will take for the rock to be ON THE GROUND. The height of anything on the ground after it falls is 0, so we sub a 0 in for h(t), since h(t) is the height of the rock at a certain time in its falling. That time is what we are solving for: the time it takes for the rock to have a height of 0.

[tex]0=-16t^2+64[/tex] and

[tex]-64=-16t^2[/tex] and

[tex]4=t^2[/tex] so

t = -2 and 2. BUT since we know that time will never be negative, then the time it takes the rock to hit the ground is

t = 2 seconds.