Question

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

Answer 1

@pooja195 @Concentrationalizing

Answer 2

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.

Answer 3

Ok, can you walk me through it? :)

Answer 4

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

Answer 5

h(0) = -16 + s?

Answer 6

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.

Answer 7

Ok :) so what next?

Answer 8

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?

Answer 9

Oh ok :D I think so.

Answer 10

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

Answer 11

Ok just give me a minute...

Answer 12

Alrighty

Answer 13

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

Answer 14

After that I don't know what to do.

Answer 15

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

Answer 16

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

Answer 17

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

Answer 18

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

Answer 19

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

Answer 20

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

Answer 21

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.

Answer 22

Oh ok! That's fine :)

Answer 23

Youre okay with doing quadratic formula correctly? :)

Answer 24

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

Answer 25

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

Answer 26

Sorry I took so long lol

Answer 27

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

Answer 28

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

Answer 29

Lol, okay. As long as it makes sense.

Answer 30

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

Answer 31

Good luck :3