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

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) (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
========================
Cheers,
Stan H.

Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Let's see if we can "un"perplex you!
Given:
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:
where h (or S) = height of object, = initial velocity, a negative means object is going down, and is the initial height of the object, so, to find the height of the object after 1 second, substitute t = 1...
Substitute t=1

feet.
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?"
Set and solve for t.
First factor (-16) to simplify the equation a bit.
so, from the zero product rule, we get...
Now factor this trinomial.
which means that...
or from which we get...
or 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 " 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).
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