Question

A firecracker shoots up from a hill 160 feet high with an initial speed of 90 feet per second. Using the formula H(t) = −16t2 + vt + s, approximately how long will it take the firecracker to hit the ground?

Answer 1

this is beyond hard!

Answer 2

thx real big help XD

Answer 3

do get awarded for this, lol?

Answer 4

I got this! Lol! 1 sec!

Answer 5

k thx jon can you show how you do it? thanks

Answer 6

First plug in the speed v they give you, 90, and i'm guessing the 160 is the s
\[\Large H(t) = −16t^2 + 90t + 160\]

The height when it reaches the ground will be zero, which means H is 0:

\[\Large 0 = −16t^2 + 90t + 160\]
Now you have to solve this, either by factoring or using the quadratic formula. To make it a little easier, you can first divide everything by 2 to get
\[\Large 0 = −8t^2 + 45t + 80\]

Answer 7

0=−16t2+105t+160

A standard quadratic is of the form
ax2+bx+c=0

its solution is given as
x=−b±b2−4ac−−−−−−−√2a

here b=105
a=-16
c=160
Let's plugin the values
x=−(105)±(105)2−4×(−16)×(160)−−−−−−−−−−−−−−−−−−−−−√2×(−16)

we get
x=−(105)±21265−−−−−√2×(−16)

x=−(105)±145.8252×(−16)

if we take + sign then t= -ve ( time can't be negative)
with - sign
x=−250.825−32

Answer 8

Quadratic formula is probably easier.. do you know how to use it? \[\Large t = \frac{ -b \pm \sqrt {b^2 - 4 ac} }{ 2a }\]

Answer 9

To get a, b and c, compare your function:
\[\Large 0=−8t^2+45t+80\]to the standard \[\Large 0=at^2+bt+c\]

Answer 10

@Jonathan1997 where did 105 come from...? Your solution isn't very easy to read...

Answer 11

in the quadractic formula on the inside of it you would have 16 -14,400 and then you get -14,416 right? but i thought things inside the radican cant be negative?

Answer 12

Okay, so you have s = 160, v = 105 so

h(t) = -16t^2 + 105t + 160, use quadratic equation to find roots of this equation, the one with a
positive t value will be your answer.

Answer 13

plug in a, b and c... from above, a=-8, b=45, c=80\[\Large t = \frac{ -45 \pm \sqrt {45^2 - 4 *(-8)*80} }{ 2(-8) }\]now simplify that, carefully, pay attention to negatives.

Answer 14

@Jonathan1997 v is not 105.

Answer 15

Okay, well I will just let agenta.s.s. help ya! GOOD LUCK!!! You will need it @Allyt

Answer 16

okayy . @agent0smith it would be 7.04375 but it would be 7 secounds right?

Answer 17

Correct.

Answer 18

*cough* *cough* sorry @agent0smith