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 200858This question is from textbook Elementary and Intermediate Algebra
: 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) = -16t2 - 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?
This question is from textbook Elementary and Intermediate Algebra

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
a)

Start with the given function.

Plug in .

Square to get .

Multiply and to get .

Multiply and to get .

Combine like terms.

So the wrench is 80 feet in the air after 1 second.

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b)

Start with the given function.

Plug in (ie make the height equal to zero).

Notice that the quadratic is 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 solutions are or

But remember that a negative time value doesn't make much sense. So we'll ignore

So the only solution is which means that it takes 2 seconds for the wrench to hit the ground.
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