- anonymous

NEED HELP ASAP. WILL FAN AND MEDAL.
A firecracker shoots up from a hill 150 feet high, with an initial speed of 110 feet per second. Using the formula H(t) = -16t^2 + vt + s, approximately how long will it take the firecracker to hit the ground?
Eight seconds
Nine seconds
10 seconds
11 seconds

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- anonymous

- anonymous

If the hill is 150 feet high, then that's essentially saying that when t = 0, h(t) should equal 150. An initial speed of 110 feet just tells you that v = 110. Using that information, you can rewrite h(t) as a quadratic in t only in which then you would just factor and solve for t.

- anonymous

Ok, can you walk me through it? :)

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## More answers

- anonymous

Well, if you plug in t = 0, what do you get?

- anonymous

h(0) = -16 + s?

- anonymous

Well, if t is 0, the -16 goes away also. \(-16(0)^{2} +v(0) + s = s\) . In the end, the problem just tells you that s = 150 and v = 110.

- anonymous

Ok :) so what next?

- anonymous

Well, that means you have \(h(t) = -16t^{2} +110t + 150\)
So, h(t) represents height. You plug in a time value and you get a height for an answer. The problem wants to know when you hit the ground. Well, if you hit the ground, then the height is 0. So we want to know what time value will make h(t) equal 0. Following me so far?

- anonymous

Oh ok :D I think so.

- anonymous

Mhm. So if h(t) needs to be 0, then you're solving this: \(-16t^{2} + 110t + 150 = 0\)

- anonymous

Ok just give me a minute...

- anonymous

Alrighty

- anonymous

Ok, I think I got lost. I only got to the beginning: -16t^2 + 110t = -150. :(

- anonymous

After that I don't know what to do.

- anonymous

Well, this is a quadratic equation, so it needs to be factored.

- anonymous

Ok, so -2t(8t - 55) = -150?

- anonymous

Nope. Have you seen before how an equation like \(x^{2} + 5x + 6\) turns into \((x+2)(x+3)\)?

- anonymous

Yes, I have. :) So I need to do that here?

- anonymous

Yeah, its that idea. So itll factor and look like ( )( ) = 0 Now it's just knowing how to factor in that way.

- anonymous

Hmm. So would it start to look like (-4t +/- ___)(-4t +/- ___)?

- anonymous

Actually, this doesnt factor cleanly. Since the question said "approximately", we won't be able to factor in the way I was thinking. We're actually forced to quadratic formula on this, I apologize.

- anonymous

Oh ok! That's fine :)

- anonymous

Youre okay with doing quadratic formula correctly? :)

- anonymous

Yes. Here give me just a few minutes ;) things around here are getting a bit crazy XD

- anonymous

Ok so is it -8.04 or 1.17?? Oh so then it would be eight seconds??

- anonymous

Sorry I took so long lol

- anonymous

I didnt do the full math, but itd be 8 seconds, yeah :3

- anonymous

Ok thanks! I'll give you a medal but I'm already a fan ;)

- anonymous

Lol, okay. As long as it makes sense.

- anonymous

Yes it does now ;) because of you. Thanks so much! Ttyl :)

- anonymous

Good luck :3

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