Expert: Sherman D. - 6/9/2008

Question
the height if a projectile upward is given by the formula S=V0T-16T (squared).  S = ht in feet, V0 = initial velocity ad T = time in seconds.  Find the time for a projectile to reach a height of 64 feet if it has an initial velocity of 128 ft/second. Round to the nearest hundredth of a second.  My stepdaughter has this question on homework and I am unable to help her.

Answer
64 = 128T - 16T^2

16t^2 - 128t + 64 = 0
16(t^2 - 8t + 4) = 0

now using the quadratic formula

t = (-(-8) ± sqrt((-8)^2 - 4(1)(4)))/(2(1))
t = (8 ± sqrt(64 - 16))/2
t = (8 ± sqrt(48))/2
t = (8 ± sqrt(16 * 3))/2
t = (8 ± 4sqrt(3))/2
t = 4 ± 2sqrt(3)
t = about 7.46 seconds and about .54 seconds