Question

A pebble falls off a cliff at a height of

1,296ft . 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 pebble
to hit the ground?
[?] seconds
Enter

Answer 1

Explanation:

The equation for this free fall problem is

`h(t)=-16t^2+1296` where h(t) is the height of the pebble from the ground at any time t. If we are looking for the time it takes the pebble to hit the ground, knowing that at ground level the height is 0, we set the quadratic equal to 0 and solve for t:

`-16t^2+1296=0` and

`-16t^2=-1296` and

`t^2=81` so

t = -8, 8

Since time will never be negative,

t = 8 seconds