Answer:
<em>4 seconds, 256 ft</em>
Step-by-step explanation:
First, we'll go through what needs to be done. Then we'll do it.
When h is 0, the fireworks is at a height of 0, or ground level. That happens before it is launched, at time 0 and when it falls back to the ground after going up and down. We let h = 0, and solve for t. We get t = 0, and another value for t which is when it hits the ground on the way down. The midpoint between the two times of height zero is the time at which maximum height is reached. Then we input the maximum height time into the equation and find h, the maximum height.
Now we'll solve it. First, we set the height equation equal to zero and solve for t.
-16t^2 + 128t = 0
-16t(t - 8) = 0
t = 0 or t - 8 = 0
t = 0 or t = 8
The height is zero at t = 0 seconds and at t = 8 seconds.
Maximum height is reached at the midpoint of the two times above.
(0 + 8)/2 = 8/2 = 4.
The firework explodes at 4 seconds.
Now we find the height at 4 seconds which is the maximum height.
h = -16t^2 + 128t
h = -16(4^2) + 128(4)
h = -256 + 512
h = 256
The firework explodes at a height of 256 ft.
