SOLUTION: The equation h=16t^2 + 112t gives the height of an arrow, shot upward from the ground with an initial velocity of 112ft/s, where t is the time after the arrow leaves the ground. F

Question 92509: The equation h=16t^2 + 112t gives the height of an arrow, shot upward from the ground with an initial velocity of 112ft/s, where t is the time after the arrow leaves the ground. Find the time it takes for the arrow to reach a height of 180ft.?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Are you sure that the equation isn't (let me know if it is otherwise)

Start with the given equation

Let h=180

Subtract 180 from both sides

Let's use the quadratic formula to solve for t:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=-16, b=112, and c=-180

Square 112 to get 12544

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and -16 to get -32

So now the expression breaks down into two parts

or

Lets look at the first part:

Add the terms in the numerator
Divide

So one answer is

Now lets look at the second part:

Subtract the terms in the numerator
Divide

So another answer is

So our solutions are:
or
which are

or

in decimal form

So it takes 2.5 seconds to rise to 180 feet. Then it takes 4.5 seconds (elapsed from the beginning) to fall back to 180 feet.

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