SOLUTION: If a rocket is fired vertically into the air with a speed of 368 feet per second, its height at time t seconds is given by h(t)=-16tsquared+368t. How long will the rocket be in th

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Question 382389: If a rocket is fired vertically into the air with a speed of 368 feet per second, its height at time t seconds is given by h(t)=-16tsquared+368t. How long will the rocket be in the air?
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
h(t)=-16t^2+368t
.
You can set h(t) to zero and solve for t:
h(t)=-16t^2+368t
0=-16t^2+368t
0=16t^2-368t
0=16t(t-23)
t = {0, 23}
answer: 23 seconds
.
OR, you can think of like:
The vertex is at it's highest point AND at mid-flight. If we found time (t) when it reaches the vertex, we simply double it for the answer.
.
time (t) at vertex:
t = -b/(2a) = -368/(2*(-16)) = -368/(-32) = 11.5 sec
.
Answer:
2*11.5 = 23 seconds
.