Question

the altitude of an object in feet is given by h=16t^2+8t+48. What is the maximum altitude ?After how many seconds "t" will it strike the ground ?

Answer 1

according to that equation; itll never hit the ground

Answer 2

then what is its maximum altitude ?

Answer 3

according to your equation; gravity will continue to push it out into infinity

Answer 4

hmmmm

Answer 5

you sure it aint -16t^2?

Answer 6

ohh lol IT IS . i read the question wrong sorry

Answer 7

:) -16t^2 is the result of gravity pulling the object back to earth ...

Answer 8

well, there are a few ways we can go about this; which ones do you know of?

Answer 9

none

Answer 10

can u please explain

Answer 11

when we plot this on a graph; we get a shape that looks like a hill, its called a parabola

Answer 12

the top of that hill is the highest point it reaches and it reaches that point in about half the time

Answer 13

since this started at a height of 48; that measurement will be off but we can account for it

Answer 14

the most basic way i know of to find the high point, also known as a vertex, is to determine what make the equation equal 0, so we factor it

Answer 15

-16t^2+8t+48 = 0 ; we can factor out a common -8 first of all

-8(2t^2 -t -6) = 0; that -8 is useless to us since -8(0) = 0.
so we can ignore it

2t^2 -t -6 = 0 ; my method employs multiplying the 1st
and 3rd #s

2(-6) = -12 ; now find factors of -12 that add up to -1 (our 2nd#)

-4*3 = -12 ; and -4+3 = -1

this gives us the factors of our equation to be:

(t-4/2) (t+3/2) = 0 ; simplify and if its a fraction left over stick
the bottom in front

(t-2) (2t+3) = 0 when t=2 or t=-3/2

lets plot these on a number line and find the middle:

t
<...........-3/2..........(C)............2..........>
1/4

when t = 1/4 we are at our highest point; and when t=2 we are back on the ground

Answer 16

another way to find the middle is to add them together and divide it in half:

2-1.5 = .5 ; .5/2 = .25

to find the height, just use .25 in the equation in the place of t and calculate

Answer 17

http://www.wolframalpha.com/input/?i=-16%28.25%29^2%2B8%28.25%29%2B48