SOLUTION: the height h(t) of a projectile measured from ground-level is given by h(t) = -t^2+8t where t represents the elapsed time in seconds since it was launched a) can the projecti

Question 651539: the height h(t) of a projectile measured from ground-level is given by
h(t) = -t^2+8t where t represents the elapsed time in seconds since it was launched
a) can the projectile hit a target located at a height of 20 cm?
b) at what instant does the projectile hit the ground?

Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
the height h(t) of a projectile measured from ground-level is given by
h(t) = -t^2+8t where t represents the elapsed time in seconds since it was launched
a) can the projectile hit a target located at a height of 20 cm?
the max height is at the vertex:
time at vertex:
t = -b/(2a)
t = -8/(2(-1))
t = -8/(-2)
t = 4 secs
.
height at vertex:
h(4) = -4^2+8(4)
h(4) = -16+32
h(4) = 32
since 32 is greater than 20, answer is yes
.
b) at what instant does the projectile hit the ground?
set h(t) to zero and solve for t:
h(t) = -t^2+8t
0 = -t^2+8t
0 = t(-t+8)
t = {0, 8}
answer: 8 seconds

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