If an object is dropped from a height of 144 feet, the function gives the height of the object after t seconds. When will the object hit the ground?

A=-32 (acceleration is the constant g) integrating with respect to t

v=-32t+vi but initial velocity is equal to zero as it is just "dropped".

h=-32t^2/2+hi, since the initial height is 144 ft

h (t) = - 16t^2+144

The object will be at the ground when h (t) = 0

-16t^2+144

-16 (t^2-9) = 0

-16 (t+3) (t-3) = 0, but since we know t>0

t=3 seconds.