SOLUTION: Can you please help me with this problem? Throwing a wrench. An angry construction worker throws his wrench downward from a height of 128 feet with an initial velocity of 32 f

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Question 304649: Can you please help me with this problem?
Throwing a wrench. 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.
a) What is the height of the wrench after 1 second?
b) How long does it take for the wrench to reach the
ground?
Found 2 solutions by josmiceli, Alan3354:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
When t+=+1 sec
S%28t%29=+-16t%5E2+-+32t+%2B+128
S%281%29=+-16%2A1%5E2+-+32%2A1+%2B+128
S%281%29+=+-16+-+32+%2B+128
S%281%29+=+80
The height above ground is 80 ft
---------------------------------
When S%28t%29+=+0 (the height above ground is zero)
-16t%5E2+-+32t+%2B+128+=+0
Solve using quadratic formula
t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+-16
b+=+-32
c+=+128

t+=+%2832+%2B-+sqrt%281024+%2B+8192+%29%29%2F%28-32%29+
t+=+%2832+%2B-+sqrt%28+9216+%29%29%2F%28-32%29+
t+=+%2832+%2B-+96%29%2F%28-32%29+
t+=+%2832+-+96%29%2F%28-32%29
t+=+%28-64%29%2F%28-32%29
t+=+2
In 2 sec the wrench will reach the ground

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
S(t)= 16t^2  32t + 128.
a) What is the height of the wrench after 1 second?
S(1) = -16 - 32 + 128
= 80 feet
------------
b) How long does it take for the wrench to reach the
ground?
16t^2  32t + 128 = 0
t^2 + 2t - 8 = 0
(t+4)*(t-2) = 0
t = 2 seconds