Question

A firecracker shoots up from a hill 140 feet high, with an initial speed of 100 feet per second. Using the formula H(t) = −16t2 + vt + s, approximately how long will it take the firecracker to hit the ground?

Five seconds
Seven seconds
Nine seconds
11 seconds

Answer 1

`initial speed of 100 feet per second` means v = 100

Answer 2

The initial height is 140 ft because `A firecracker shoots up from a hill 140 feet high`
so s = 140

Answer 3

\[\Large H(t) = -16t^2+vt+s\]
turns into
\[\Large H(t) = -16t^2+100t+140\]
making sense so far?

Answer 4

so in so..

Answer 5

i think it would be 7 @jim_thompson5910

Answer 6

Did you use the quadratic formula to solve?

Answer 7

so in so...

Answer 8

i thought it would be 7 or 9

Answer 9

did you get a decimal result?

Answer 10

I'm curious to see what you got before you rounded

Answer 11

tbh it was a guess..

Answer 12

Looking at
\[\Large H(t) = -16t^2+100t+140\]
do you agree that
a = -16
b = 100
c = 140
??

Answer 13

whats a,b,c

Answer 14

like howd you get that?

Answer 15

\[\Large {\color{red}{-16}}t^2+{\color{green}{100}}t+{\color{blue}{140}}\]
is in the form
\[\Large {\color{red}{a}}t^2+{\color{green}{b}}t+{\color{blue}{c}}\]

where
\[\Large \color{red}{a = -16}\]
\[\Large \color{green}{b = 100}\]
\[\Large \color{blue}{c = 140}\]

Answer 16

oh

Answer 17

make sense?

Answer 18

yes

Answer 19

so you'll plug
a = -16
b = 100
c = 140
into the quadratic formula
\[\Large x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\]

Answer 20

okay

Answer 21

tell me what two results you get. You should get decimal values

Answer 22

ik how to plug them in but i dont know how to solve... @jim_thompson5910

Answer 23

You have this so far?
\[\Large x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\]
\[\Large x = \frac{-100\pm\sqrt{100^2-4*(-16)*(140)}}{2*(-16)}\]

Answer 24

so we solve?

Answer 25

what is 100^2 equal to?

Answer 26

10000

Answer 27

yes

Answer 28

how about 4*(-16)*(140) ?

Answer 29

-8960?

Answer 30

So
\[\Large x = \frac{-100\pm\sqrt{100^2-4*(-16)*(140)}}{2*(-16)}\]
turns into
\[\Large x = \frac{-100\pm\sqrt{10,000-(-8,960)}}{2*(-16)}\]

Answer 31

\[\Large x = \frac{-100\pm\sqrt{10,000-(-8,960)}}{2*(-16)}\]
turns into
\[\Large x = \frac{-100\pm\sqrt{10,000+8,960}}{2*(-16)}\]

Answer 32

and the bottom is -32?

Answer 33

correct

Answer 34

okay so the top is -1140 and the bottom is -32?

Answer 35

10,000+8,960 = ???

Answer 36

18960

Answer 37

take the square root of that to get what?

Answer 38

??

Answer 39

\[\Large \sqrt{18,960} = ???\]

Answer 40

type `sqrt(18960)` into a calculator

http://web2.0calc.com/

Answer 41

okay

Answer 42

tell me what you get for the result of sqrt(18960)

Answer 43

137.695315824468045

Answer 44

good

Answer 45

im sorry this is taking forever

Answer 46

so we have this now
\[\Large x \approx \frac{-100\pm137.695315824468045}{-32}\]

Answer 47

that's ok. It's good not to rush

Answer 48

so we divide -32

Answer 49

break up the plus/minus to get these two equations
\[\Large x \approx \frac{-100+137.695315824468045}{-32}\]
OR
\[\Large x \approx \frac{-100-137.695315824468045}{-32}\]

Answer 50

Simplify the top first, then divide by -32

Answer 51

okay i got 4.3..

Answer 52

let's focus on the "plus" first
\[\Large x \approx \frac{-100+137.695315824468045}{-32}\]
\[\Large x \approx \frac{37.695315824468}{-32}\]
\[\Large x \approx -1.17797861951462\]
\[\Large x \approx -1.178\]

Answer 53

agreed? or no?

Answer 54

yes

Answer 55

ok let's focus on the "minus" now
\[\Large x \approx \frac{-100-137.695315824468045}{-32}\]
\[\Large x \approx \frac{-237.695315824468}{-32}\]
\[\Large x \approx 7.42797861951462\]
\[\Large x \approx 7.428\]

Answer 56

so seven?

Answer 57

So the two solutions to \[\Large -16t^2+100t+140=0\] are
\[\Large t \approx -1.178 \ \ \text{ or } \ \ t \approx 7.428\]

Answer 58

the negative time value makes no sense, which means we ignore it

Answer 59

yes approx 7 seconds

Answer 60

okay thank you im sorry that i took so long

Answer 61

that's ok