SOLUTION: 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 abo
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Question 275603: 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 solver91311(24713) (Show Source): You can put this solution on YOUR website!
Your height function is improperly stated.
\ =\ \frac{1}{2}gt^2\ +\ v_ot\ +\ s_o)
Where 
is the acceleration in feet per second due to gravity, namely 
and 
is the initial velocity, here 
and 
is the initial height, here 128 feet.
Hence:
\ =\ -16t^2\ +\ (-32)t\ +\ 128)
The height of the wrench after 1 second is the value of the function when 
. Plug in the value and do the arithmetic:
\ =\ -16(1)^2\ +\ (-32)(1)\ +\ 128)
The height of the ground is zero, so the time value when \ =\ 0)
is the length of time it takes for the wrench to hit the ground -- presuming that the wrench didn't hit something else, perhaps the worker's boss' head -- before it hit the ground. So, solve the quadratic:
t\ +\ 128\ =\ 0)
Hint: First factor out -16
John
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