SOLUTION: Please help me with this one, I think I have the solution but not sure. An explosion causes debris to rise vertically. The funtion f(t)=-16^2 + 72t describes the height of the de

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Please help me with this one, I think I have the solution but not sure. An explosion causes debris to rise vertically. The funtion f(t)=-16^2 + 72t describes the height of the de      Log On

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Question 380973: Please help me with this one, I think I have the solution but not sure.
An explosion causes debris to rise vertically. The funtion f(t)=-16^2 + 72t describes the height of the debris above the ground, f(t), in feet, t seconds after the explosion.
When does the debris reach its maximum height: I got (-72/-32, 81)
What is the maximum height of the debris: I got (25/2, 81)
When does the debris hit the ground? I got -9/2
When we do these she tells us for the first two to use b/2(a) and then then last one I did the quadratic equation.
Please help me with this so I can work some more on this packet.
Thank you so very much
Tracy
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
First, let's get the equation right!
f%28t%29+=+-16t%5E2%2B72t
1) The time to reach maximum height is given by:
t%5Bmax%5D+=+-b%2F2a
t%5Bmax%5D+=+-72%2F2%28-16%29
t%5Bmax%5D+=+9%2F4seconds.
2) The maximum height can be found by substituting the time t%5Bmax%5D+=+9%2F4seconds into the given equation.
h%5Bmax%5D+=+-16t%5E2%2B72t Substitute t%5Bmax%5D+=+9%2F4
h%5Bmax%5D+=+-16%289%2F4%29%5E2%2B72%289%2F4%29 Evaluate.
h%5Bmax%5D+=+-16%2881%2F16%29%2B162
h%5Bmax%5D+=+81feet.
3) The time whe debris will hit the ground (h+=+0) can be found by setting the given equation f(t)= 0 and solving for the time, t.
-16t%5E2%2B72t+=+0 Factor out a t.
t%28-16t%2B72%29+=+0 Now apply the zero product rule:
t+=+0 or %28-16t%2B72%29+=+0
The t+=+0 solution is the initial condition.
-16t%2B72+=+0 Subtract 72 from both sides.
-16t+=+-72 Divide both sides by -16.
t+=+9%2F2
t+=+4.5seconds.