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

Question 121298: Science and medicine:
The equation h = -16t^2 + 112t gives the height of an arrow, shot upward from the ground with an initial velocity of 112 ft/s, where t is the time after the arrow loeaves the ground. Find the time it takes for the arrow to reach a height of 180 ft.
I would really appreciate some help on this, Thank you very much.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation

Plug in

Get everything to the left side

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

Negate -112 to get 112

Square -112 to get 12544 (note: remember when you square -112, you must square the negative as well. This is because .)

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 respectively in decimal form)

So it takes 2.5 seconds for the arrow to climb to 180 ft and then 4.5 seconds for the arrow to fall back to 180 ft

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