Question

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?

Answer 1

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