Question

James jumped off a cliff into the ocean in Acapulco while vacationing with friends. His height as a function of time is modeled as:

h(x)=-16t^2+16t+480

t is time (seconds) and h is height (feet)

How long did it take James to reach Max height?

I definitely need help with this

Answer 1

Ok our equation is in standard form
\[ax^2+bx+c\]
Where our a=-16, b=16 and c=480

Our maximum point occurs at the vertex
We know that the x coordinate of our vertex can be found using the following equation
\[\frac{-b}{2a}\]
Using this equation what would our x-coordinate of our vertex be?

Answer 2

\[\frac{ 1 }{ 2 }\]

Answer 3

So now we have found that the vertex occurs at t=1/2 or in other words at a half a second we reach the maximum height. Now in order to find the height we need to plug into our equation t=1/2 and we will find the maximum height.

Answer 4

How would you go about finding how long it took for James to hit the water?

Answer 5

Ok when you hit the water the height is 0
So plug in 0 as height and then solve for t to find at the time you hit the water

Answer 6

Oh yeah!! Duh lol I'm so sleepy xD Thanks mate!

Answer 7

Same here. I can barely function. Not sure why I am on here

Answer 8

Haha