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) About Me  (Show Source):
You can put this solution on YOUR website!


Your height function is improperly stated.



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:



The height of the wrench after 1 second is the value of the function when . Plug in the value and do the arithmetic:



The height of the ground is zero, so the time value when 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:



Hint: First factor out -16

John