Question 194925: 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?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! 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?
Substitute 1 for t and find S(t)
S(t) = -16(1^2) - 32(1) + 128
S(t) = -16 - 32 + 128
S(t) = 80 ft after 1 sec
:
:
b) How long does it take for the wrench to reach the
ground?
The ground, S(t) = 0, so we have
-16t^2 - 32t + 128 = 0
Simplify, divide equation by -16, this changes the signs, makes it easy factor:
t^2 + 2t - 8 = 0
Factors to
(t + 4)(t - 2) = 0
the positive solution
t = 2 secs to hit the ground
:
:
you can check this. Substitute 2 for t in the original equation, find S(t)
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