SOLUTION: Science and medicine. The equation h=-16t^2+112t gives the height of an arrow, shot upward from the ground with an initial velocity of 112 ft/s, where t is the time after the arro

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Question 97604: Science and medicine. The equation h=-16t^2+112t gives the height of an
arrow, shot upward from the ground with an initial velocity of 112 ft/s, where t is the time after the arrow leaves the ground. Find the time it takes for the arrow to reach a height of 180 ft.Solve to the nearest thousandth.
Please help me. I need to show all of the work and I am stumped. I have a horrible problem with word problems.
Thank you very much for your help.
Found 2 solutions by Earlsdon, stanbon:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Well, you have given the of height (h) as a function of time (t) as:
h%28t%29+=+-16t%5E2%2Bv%5B0%5Dt%2Bh%5B0%5D where v%5B0%5D+=+112ft/sec, and h%5B0%5D+=+0.
So what you are asking for is at what time, t, will h = 180 ft? Right?
Substituting h = 180, you can solve for t.
180+=+-16t%5E2%2B112t Subtract 180 from both sides.
-16t%5E2%2B112t-180+=+0 Simplify this by factoring a -4.
-4%284t%5E2-28t%2B45%29+=+0 Factor trinomial in the parentheses.
-4%282t-5%29%282t-9%29+=+0 Apply the zero products principle.
2t-5+=+0 or 2t-9+=+0 then:
2t+=+5 or 2t+=+9 so...
t+=+2.5 or t+=+4.5
The answer to the question..."At what time will the arrow reach a height of 180 ft?"
It will reach a height of 180 ft in 2.5 seconds on the way up and again at 4.5 seconds on the way down.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The equation h=-16t^2+112t gives the height of an arrow, shot upward from the ground
with an initial velocity of 112 ft/s,
where t is the time after the arrow leaves the ground.
Find the time it takes for the arrow to reach a height of 180 ft.Solve to the nearest thousandth.
------------------
h(t) = -16t^2+112t
Let h(t)= 180 ft and solve for "t":
-16t^2+112t=180
-16t^2+112t-180 = 0
Divide thru by -4 to get:
4t^2 -28t + 45 = 0
Use the quadratic formula to get:
t = [28 +- sqrt(28^2 - 4*4*45)]/8
t = [28 +- sqrt64)]/8
t = [28 +- 8]/8
t = (28+8)/8 = 4.5 seconds (time when the arrow is on the way down)
t = (28-8)/8 = 2.5 seconds (time when the arrow is on the way up)
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Cheers,
Stan H.