SOLUTION: I need help with this word problem about velocity please. An angry construction worker throws his wrench downward from a height of 128 feet with an initial velocity of 32 feet p

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Question 204099: I need help with this word problem about velocity please.
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?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+S%28t%29=+-16t%5E2-32t%2B128
Looking at the equation, when t+=+0,
S%28t%29+=+128 as it should
When S%28t%29+=+0, that is when the
wrench hits the ground
I can find t by
0+=+-16t%5E2+-+32t+%2B+128
Divide both sides by 16
-t%5E2+-+2t+%2B+8+=+0
Use the qudratic equation
t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+-1
b+=+-2
c+=+8
t+=+%28-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%2A%28-1%29%2A8+%29%29%2F%282%2A%28-1%29%29+
t+=+%282+%2B-+sqrt%28+4+%2B+32+%29%29%2F%28-2%29%29+
t+=+%282+%2B-+6%29%2F%28-2%29
t+=+-4 (not possible)
t+=+2 answer
It takes 2 sec for the wrench to hit the ground
after 1 sec,
+S%28t%29=+-16t%5E2-32t%2B128
+S%281%29=+-16%2A1%5E2-32%2A1%2B128
S%281%29+=+-16+-+32+%2B+128
S%281%29+=+80
After 1 sec, the wrench is 80 ft above the ground