SOLUTION: 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 t

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Question 333790: 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 t seconds is given by S (t) =-16t 2 -32t +128. What is the height of the wrench after 1 second? How long does it take for the wrench to reach the ground?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
S%28t%29+=+-16t%5E2-32t%2B128
To find the height after 1 second, substitute S = 1 and solve.
S%281%29+=+-16%281%29%5E2-32%281%29%2B128 Solve for S.
S%281%29+=+-16-32%2B128 simplify.
S%281%29+=+-48%2B128
S%281%29+=+80
The wrench's height is 80 ft. after 1 second.
To find how long it takes for the wrench to reach the ground (height = 0), set the given equation equal to zero and solve for t.
0+=+-16t%5E2-32t%2B128 Factor out -16 to simplify this quadratic equation a bit.
-16%28t%5E2%2B2t-8%29+=+0 Now solve:
t%5E2%2B2t-8+=+0 Factor.
%28t-2%29%28t%2B4%29+=+0 Apply the zero products rule.
t-2+=+0 or t%2B4+=+0 so...
highlight%28t+=+2%29 or cross%28t+=+-4%29 Discard the solution since the time, t, will be positive.
The wrench will hit the ground iin 2 seconds.