A rock is projected directly upward from ground level with an initial velocity of 90 ft/sec. After how many seconds will it return to the ground?

For this case we have the following equation of motion:

h (t) = - 16t ^ 2 + 90t

Equaling the equation to zero we have:

-16t ^ 2 + 90t = 0

We look for the roots of the polynomial:

(t) ( - 16t + 90) = 0

t1 = 0 (initial position)

t2 = 90/16 = 5.625 s (time it reaches the ground again)

Answer:

it will return to the ground in:

t = 5.625 s