SOLUTION: Help. I'm totally perplexed by the question: An angry construction worker throws his wrench downward from a height of 128 feet with an initial velocity of 32 feet per second. The h

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: Help. I'm totally perplexed by the question: An angry construction worker throws his wrench downward from a height of 128 feet with an initial velocity of 32 feet per second. The h      Log On


   

Question 276918: Help. I'm totally perplexed by the question: An angry construction worker throws his wrench downward from a height of 128 feet with an initial velocity of 32 feet per second. The height of the wrench above the ground after 6 seconds is given by S(t) = -16t^2 -32t +128.
What is the height after 1 second? How long does it take for the wrench to reach the ground?
Found 2 solutions by stanbon, Earlsdon:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
An angry construction worker throws his wrench downward from a height of 128 feet with an initial velocity of 32 feet per second.
The height of the wrench above the ground after 6 seconds is given by
S(t) = -16t^2 -32t +128.
What is the height after 1 second?
S(1) = -16-32+128 = 80 ft.
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How long does it take for the wrench to reach the ground?
Solve -16t^2 -32t + 128 = 0
Divide thru by -16 to get:
t^2 + 2t - 8 = 0
---
(t+4)(t-2) = 0
Positive solution:
t = 2 seconds
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Cheers,
Stan H.

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let's see if we can "un"perplex you!
Given:
S%28t%29+=+-16t%5E2-32%2B128 This is the quadratic equation that shows the relationship of the height (h or S) of an object as a function of time (t).
The general form is:
h%28t%29+=+-%281%2F2%29gt%5E2+%2Bv%5B0%5Dt%2Bh%5B0%5D where h (or S) = height of object, v%5B0%5D= initial velocity, a negative v%5B0%5D means object is going down, and h%5B0%5Dis the initial height of the object, so, to find the height of the object after 1 second, substitute t = 1...
S%28t%29+=+-16t%5E2-32t%2B128 Substitute t=1
S%281%29+=+-16%281%29%5E2-32%281%29%2B128
S%281%29+=+-48%2B128
S%281%29+=+80feet.
The hammer (or was it a wrench?) would be 80 feet above the ground after 1 second had elapsed.
The second question...How long does it take for it (the wrench) to reach the ground? So you are really asking..."At what time t will the height S be zero?"
S%28t%29+=+-16t%5E2-32t%2B128 Set S%28t%29+=+0 and solve for t.
-16t%5E2-32t%2B128+=+0 First factor (-16) to simplify the equation a bit.
-16%28t%5E2%2B2t-8%29+=+0 so, from the zero product rule, we get...
t%5E2%2B2t-8+=+0 Now factor this trinomial.
%28t%2B4%29%28t-2%29+=+0 which means that...
t%2B4+=+0 or t%2B2+=+0 from which we get...
t+=+-4 or highlight%28t+=+2%29 Discard the negative solution.
So it would take 2 seconds for the wrench to reach the ground.
P.S. Your statement "The height of the wrench above the ground after 6 seconds is given by S%28t%29+=+-16t%5E2-32T%2B128" does not make sense. The equation is ok but this will tell you the height above ground after t seconds.
To find the height above ground after 6 seconds, you would have to substitute t = 6 into the equation and solve for S(6).