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

Question 180814: 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?

Found 2 solutions by jim_thompson5910, eperette:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
a)
Start with the given equation.

Plug in .

Square to get .

Multiply and to get .

Multiply and to get .

Combine like terms.

So after one second, the wrench is 80 ft above the ground.

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b)

The wrench will reach the ground when (ie the height of the wrench is zero)

Start with the given equation.

Plug in

Notice we have a quadratic equation in the form of where , , and

Let's use the quadratic formula to solve for t

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Rewrite as

Add to to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the possible answers are or

However, you CANNOT have a negative time. So the only answer is

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Answer:

So it takes 2 seconds for the wrench to hit the ground
Answer by eperette(173) (Show Source): You can put this solution on YOUR website!
S(t)= -16t^2 -32t + 128
(a) need to find S(t) when t=1
S(1)= -16(1)^2 - 32(1) + 128
S(1)= -16 -32 + 128
S(1)= 80
At t=1second the height of the wrench is 80ft
(b)if the wrench reaches the ground, then the height is 0, ...in other words it is asking you to find t when S(t)=0....you can solve this problem two ways
(Graphing Method)
With your calculator, graph the equation...your solution will be your zeros (or x-intercepts)....notice that x-intercepts happen at t=-4 and t=2....t=-4 does not make sense so your answer should be t=2 seconds
(Algebra Method)
0 = -16t^2 - 32t +128
0 = t^2 -32t -2048
0 = (t-64)(t+32)
0 = (t-64/-16)(t + 32/-16)
0 = (t + 4)(t-2)
(t+4)=0 or (t-2)=0
t=-4 or t=2
it would not make sense of the time to be negative....so this leaves us with one answer: the wrench reaches the ground when t=2 seconds
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