Question

a ball is thrown upward from a 100-foot tall building with an initial velocity of 14 feet per second, find the interval of time which the ball is greater than 103 feet. s(t)=-16t^+14t+100????

Answer 1

is this the "full" problem? the question did not explain what the equation meant?

Answer 2

it can mean something else sometimes

Answer 3

it says the height s(t) is given by this function.

Answer 4

ahh better

Answer 5

so when height is 103 feet then s(t) would be 103 do you agree?

Answer 6

i would think so

Answer 7

well s(t) would be 103 because it says the height is 103 and s(t) is the height. do you get the logic? you need to understand that part because it is crucial ;)

Answer 8

so s(t) = 103

that means \[-16t^2 + 14t + 100 = 103\]
\[-16t^2 + 14t + 100 - 103 = 0\]
\[-16t^2 + 14t - 3 = 0 \]
do you get it so far?

Answer 9

ok yes i see that

Answer 10

good. now you use the quadratic formula to solve for t. i assume you're familiar with the formula yes?

Answer 11

somewhat

Answer 12

great.
\[t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\]
tell me what you get after you solve it :D

Answer 13

-14 square root 4/32

Answer 14

and what is the square root of 4?

Answer 15

2

Answer 16

btw...32 should be negative.. 2 x -16 = -32

Answer 17

\[\frac{-14 \pm \sqrt 4}{-32} \implies \frac{-14 \pm 2}{-32}\]

Answer 18

Thank you so much.

Answer 19

ahh you got the answer already?

Answer 20

No so i assume it needs to be simplified?

Answer 21

yup..

i can break it down into two parts
\[\frac{-14 + 2}{-32}\]
and
\[\frac{-14 - 2}{-32}\]

Answer 22

solve for those two and you'll get the answer

Answer 23

ok -3/8 and -1/2 ????

Answer 24

nope..remember negative divided by negative is positive

also you cant have negative time

Answer 25

ahhh 3/8 and 1/2

Answer 26

yup

Answer 27

you are awesome thank you so much....

Answer 28

<tips imaginary hat>