SOLUTION: My problem is: An arrow is shot from the top of a 144 foot tower with an initial velocity of 128 feet per second. The height of the arrow, h feet, after t seconds is given by the

Question 92401: My problem is:
An arrow is shot from the top of a 144 foot tower with an initial velocity of 128 feet per second. The height of the arrow, h feet, after t seconds is given by the equation.
h=-16t^2+128t+144
a. If the arrow reaches its maximum height in 4 seconds, find its maximum height.
b. How many seconds will it take for the arrow to reach the ground?

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
"a. If the arrow reaches its maximum height in 4 seconds, find its maximum height"

Lets find when

Start with the given polynomial

Plug in

Raise 4 to the second power to get 16

Multiply -16 by 16 to get -256

Multiply 128 by 4 to get 512

Now combine like terms

So when ,

So the maximum height is 400 feet

"b. How many seconds will it take for the arrow to reach the ground?"

Let h=0 and solve for t

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=128, and c=144

Square 128 to get 16384

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 possible solutions are:
or

However, a negative time doesn't make sense. So our only answer is

So it takes 9 seconds to reach the ground
RELATED QUESTIONS
An arrow is shot directly upward from the top of a 112-foot tall building with an initial (answered by stanbon)

An arrow is launched upward with a velocity of 128 feet per second from the top of a... (answered by josmiceli)

Can you help solve this? An arrow is shot upward and outward from atop a 81-foot... (answered by ankor@dixie-net.com)

an object is thrown upward from the top of a 144-foot building with a initial velocity of (answered by josmiceli)

An object is thrown upward from the top of a 144-foot building with and initial velocity... (answered by ewatrrr)

A ball is thrown vertically upward from the top of a building 144 feet tall with an... (answered by KnightOwlTutor)

fireworks are shot upward with an initial velocity of 128 feet per second from a platform (answered by Alan3354)

Please, please help me, I have been working on this problem for 1 1/2 hours and cannot... (answered by stanbon,edjones)

An arrow is fired into the air with an initial velocity of 128 feet per second. The... (answered by Alan3354)