anonymous
  • 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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
@pooja195 @Concentrationalizing
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
  • anonymous
Ok, can you walk me through it? :)

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anonymous
  • anonymous
Well, if you plug in t = 0, what do you get?
anonymous
  • anonymous
h(0) = -16 + s?
anonymous
  • 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
  • anonymous
Ok :) so what next?
anonymous
  • 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
  • anonymous
Oh ok :D I think so.
anonymous
  • anonymous
Mhm. So if h(t) needs to be 0, then you're solving this: \(-16t^{2} + 110t + 150 = 0\)
anonymous
  • anonymous
Ok just give me a minute...
anonymous
  • anonymous
Alrighty
anonymous
  • anonymous
Ok, I think I got lost. I only got to the beginning: -16t^2 + 110t = -150. :(
anonymous
  • anonymous
After that I don't know what to do.
anonymous
  • anonymous
Well, this is a quadratic equation, so it needs to be factored.
anonymous
  • anonymous
Ok, so -2t(8t - 55) = -150?
anonymous
  • anonymous
Nope. Have you seen before how an equation like \(x^{2} + 5x + 6\) turns into \((x+2)(x+3)\)?
anonymous
  • anonymous
Yes, I have. :) So I need to do that here?
anonymous
  • anonymous
Yeah, its that idea. So itll factor and look like ( )( ) = 0 Now it's just knowing how to factor in that way.
anonymous
  • anonymous
Hmm. So would it start to look like (-4t +/- ___)(-4t +/- ___)?
anonymous
  • 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
  • anonymous
Oh ok! That's fine :)
anonymous
  • anonymous
Youre okay with doing quadratic formula correctly? :)
anonymous
  • anonymous
Yes. Here give me just a few minutes ;) things around here are getting a bit crazy XD
anonymous
  • anonymous
Ok so is it -8.04 or 1.17?? Oh so then it would be eight seconds??
anonymous
  • anonymous
Sorry I took so long lol
anonymous
  • anonymous
I didnt do the full math, but itd be 8 seconds, yeah :3
anonymous
  • anonymous
Ok thanks! I'll give you a medal but I'm already a fan ;)
anonymous
  • anonymous
Lol, okay. As long as it makes sense.
anonymous
  • anonymous
Yes it does now ;) because of you. Thanks so much! Ttyl :)
anonymous
  • anonymous
Good luck :3

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