a ball is thrown upward with an initial velocity of 64 ft/s from a height 512 ft. h= -16t^2+64t+512. after how many seconds will the ball reach the ground? (i.e. for what positive value of t is h=0?)

Given:

h= -16t^2+64t+512

Set h to 0 and solve for t:

0 = -16t^2+64t+512

multiplying both sides by 1:

0 = 16t^2-64t-512

dividing both sides by 16:

0 = t^2-4t-32

factoring:

0 = (t+4)(t-8)

t = {-4, 8}

throw out the negative solution (extraneous) leaving

t = 8 seconds