# SOLUTION: Help. I'm totally perplexed by the question: An angry construction worker throws his wrench downward from a height of 128 feet with an initial velocity of 32 feet per second. The h

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 Question 276918: Help. I'm totally perplexed by the question: 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 6 seconds is given by S(t) = -16t^2 -32t +128. What is the height after 1 second? How long does it take for the wrench to reach the ground?Found 2 solutions by stanbon, Earlsdon:Answer by stanbon(60778)   (Show Source): You can put this solution on YOUR website!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 6 seconds is given by S(t) = -16t^2 -32t +128. What is the height after 1 second? S(1) = -16-32+128 = 80 ft. ---------------------------------- How long does it take for the wrench to reach the ground? Solve -16t^2 -32t + 128 = 0 Divide thru by -16 to get: t^2 + 2t - 8 = 0 --- (t+4)(t-2) = 0 Positive solution: t = 2 seconds ======================== Cheers, Stan H. Answer by Earlsdon(6294)   (Show Source): You can put this solution on YOUR website!Let's see if we can "un"perplex you! Given: This is the quadratic equation that shows the relationship of the height (h or S) of an object as a function of time (t). The general form is: where h (or S) = height of object, = initial velocity, a negative means object is going down, and is the initial height of the object, so, to find the height of the object after 1 second, substitute t = 1... Substitute t=1 feet. The hammer (or was it a wrench?) would be 80 feet above the ground after 1 second had elapsed. The second question...How long does it take for it (the wrench) to reach the ground? So you are really asking..."At what time t will the height S be zero?" Set and solve for t. First factor (-16) to simplify the equation a bit. so, from the zero product rule, we get... Now factor this trinomial. which means that... or from which we get... or Discard the negative solution. So it would take 2 seconds for the wrench to reach the ground. P.S. Your statement "The height of the wrench above the ground after 6 seconds is given by " does not make sense. The equation is ok but this will tell you the height above ground after t seconds. To find the height above ground after 6 seconds, you would have to substitute t = 6 into the equation and solve for S(6).