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

Algebra ->  Quadratic Equations and Parabolas -> 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      Log On


   

Question 275431: 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 jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
S%28t%29=+-16t%5E2+-+32t+%2B+128
a) What is the height of the wrench after 1 second?
Just replace t on the right side with a 1 and simplify. I'll leave that up to you.
b) How long does it take for the wrench to reach the ground? Another way to word this is: "What value of t makes S(t) zero?" So we need to solve:
0+=+-16t%5E2+-+32t+%2B+128
Since the left side is zero (an important part of solving quadratic equations) we can proceed to the next stage of the solution. Next we can either factor the right side or use the Quadratic Formula. This expression factors pretty easily. I'll start by factoring out a -16:
0+=+-16%28t%5E2+%2B+2t+-+8%29
And then the trinomial (three-term expression) factors:
0+=+-16%28t+%2B+4%29%28t+-2%29
From the Zero Product Property we know that this product is zero only if one of the factors is zero. -16 cannot be zero but the other two could be. So:
t%2B4+=+0 or t-2+=+0
Solving these we get:
t+=+-4 or t+=+2

Since t represents time, a time of -4 makes no sense. It would mean that the wrench was on the ground 4 seconds before the wrench was thrown. So we must reject the x = -4 solution. The only practical solution to part (b) is: After 2 seconds the wrench will be on the ground.