Justin Is Skeet Shooting During The Olympic Trails . The Height Of The Skeet is Modeled By The Equation : H: -5t^2 + 32t + 2 , Where H Is The Height iN Meters t Seconds After The Skeet Is Released . The Path Of Justins Bullet Is Modeled By The Equation : H=31.5t + 1 With The Same Units. How Long Does It Take For The Bullet To Hit The Skeet ? How High Off The Ground Will The Skeet Be When Its Been Hit? @jtvatsim

- anonymous

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- anonymous

Hello There .

- anonymous

Welcome Back :)

- jtvatsim

Hey! Alright, so if you read the question slowly (not too fast or you'll freak yourself out), you should probably notice that this is very familiar to the other problem we did, so same steps as last time. :)

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- anonymous

Yes It Is Very Similar .

- jtvatsim

1) Set equations equal (we want to see if the height of the skeet and bullet are ever the same)
2) Solve with quadratic formula. (Good ole, quadratics...)

- anonymous

-5t^2 + 32t +2 =31.5t+1

- jtvatsim

Very good! We are off to a great start with that.

- jtvatsim

So, what's next? :)

- anonymous

Then We Add And Subtract'

- jtvatsim

Yes. In this case, both numbers are positive so we subtract them to get 0 (do the opposite). The details are like this:
-5t^2 + 32t +2 =31.5t+1
-5t^2 + 32t +2 - 31.5t - 1 =31.5t+1 - 31.5t - 1 (subtracting from both sides to get 0)
-5t^2 + 32t - 31.5t + 2 - 1 = 0
-5t^2 + 0.5t + 1 = 0

- anonymous

Right

- jtvatsim

Most people simplify this in their mind by just saying "do the opposite," but I am just showing what really happens. :)

- anonymous

I Like The Way You Teach

- jtvatsim

Thanks! Glad it's helping you! OK, so now you've got your equation set to 0, so our magic quadratic formula is allowed to come forth!

- jtvatsim

This will take me a minute, I tend to be slow with this part... :)

- anonymous

Us Both Lets Take Our Time

- jtvatsim

OK, first one I'm seeing is t = -0.4... at least the decimals aren't quite as bad as last time.

- anonymous

I Was Off A Little

- jtvatsim

What did you get out of curiosity?

- anonymous

-3.9

- anonymous

I Used A Calculator

- jtvatsim

Ah, I see! Probably just a calculator slip or parenthesis missing or something. Just for reference I'm using
a = -5
b = 0.5
c = 1

- jtvatsim

\[\frac{-0.5\pm \sqrt{0.5^2 - 4(-5)(1)}}{2(-5)}\]

- anonymous

Your Right I Messed Up With Parenthesis

- jtvatsim

Cool, at least you found the issue. Parenthesis always got me when I did these before. :P

- jtvatsim

How about the other solution? Let me know what you get once you find it. Take your time. :)

- anonymous

Ok

- anonymous

X:-0.4

- anonymous

x1=0.5

- jtvatsim

Awesome, I got those two as well. :)

- jtvatsim

Now, which one is the right one? Let's think and look at what the question is talking about again...

- jtvatsim

It says, "How long does it take..."
We could say "negative 0.4 seconds" which is kind of weird....
or "0.5 seconds" which makes a lot more sense.
As another option, we could also check the equations with our answers like we did last time.

- anonymous

Yes I Think That Would Be A Great idea To Check

- jtvatsim

OK, well I just know you want to use the -5t^2 one, but restrain yourself and probably pick the simpler equation... :P

- jtvatsim

Actually, you are even more on to the question than me. It does ask for the height after all, so checking the equations will tell us the height that we need. :)

- anonymous

I Believe 0.5 Is The Correct 1

- jtvatsim

I'm seeing:
h = 31.5(-0.4) + 1 = -11.6 at t = -0.4
but,
h = 31.5(0.5) + 1 = 16.75 at t = 0.5
Yes, I agree, the bullet being underground doesn't make sense (yet... until they invent new technology)

- jtvatsim

Nice work! Getting the hang of it?

- anonymous

Sort Of When Im Being Walked Through Makes Me Think ALOT More . Are You Up For More ?

- jtvatsim

I know what you mean. It is less scary when you have a "guide" leading the way through the math jungle. :) Soon enough, you'll be able to think step by step on your own and help other people out too. Just takes practice.
Sure let's take a look! I'll be waiting.

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