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Question

An object is projected vertically upward at an initial velocity of 64 feet per second from a height of 192 feet, so that the height h at any time t is given by h= -16t²+64t+192, where t is the time in seconds. After how many seconds is the height 256 feet?

Answer 1

h(t) = -16t² + 64t + 192

Set h = 256 and solve for t.

-16t² + 64t + 192 = 256

-16t² + 64t - 64 = 0

t² - 4t + 4 = 0

(t - 2)² = 0

t = 2 seconds

Test the answer.