A Punter Kicks A Football . Its Height (h) in meters ,t seconds after the kicks is given by the equation :h=-4.9t^2 + 18.24t +0.8 . The Height Of An Approaching Blockers Hands Is Modeled By Equation : h=-1.43t + 4.26 , using the same time . Can The Blocker Knock Down The Punt ? If So , At What Time Does It Happen ?

- anonymous

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- jamiebookeater

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- jtvatsim

This one is a little tricky, but I think the plan should be:
1) Set the equations equal to each other (we want to see if the football touches the hands).
2) We will probably need to use the quadratic formula to solve.
Do you want to give that a try? I'll help guide you through it.

- anonymous

yes

- jtvatsim

Alright, let's start with the first step. We will set the equations equal to start:
-4.9t^2 + 18.24t + 0.8 = -1.43t + 4.26

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- jtvatsim

Now, we should probably try to set the equation equal to zero. I'd suggest moving the -1.43t + 4.26 to the other side, like this:

- jtvatsim

-4.9t^2 + 19.67t +5.06 = 0
Do you see how I got that?

- anonymous

Umm I Think So

- anonymous

Adding Correcct? 1.43 + 4.26 TO BOTH SIDES

- jtvatsim

Oh wait, lol. Good catch. I was supposed to add the 1.43t, but subtract the 4.26. Sorry about that. :)

- jtvatsim

-4.9t^2 + 19.67t - 3.46 = 0
There... that's better. :P

- jtvatsim

That should make more sense now. OK so far?

- anonymous

YES

- jtvatsim

Excellent! Alright, now for the "ugly" part. We have really nasty decimal numbers here, so we should probably just use the quadratic formula. Do you remember the formula or should we look it up?

- anonymous

i Remember

- jtvatsim

Alright, so I'll trust you and spare you the pain of typing it all out. I will go ahead and plug the numbers into the formula, and we can compare answers after. :)

- jtvatsim

What we can definitely say is that:
a = -4.9
b = 19.67
and c = -3.46
for when we plug in.

- jtvatsim

\[\frac{-b\pm\sqrt{b^2-4ac}}{2a} = \frac{-19.67\pm\sqrt{19.67^2-4(-4.9)(-3.46)}}{2\cdot -4.9}\]

- anonymous

Exactly Correct

- jtvatsim

Perfect! Now to simplify that horrid looking nightmare. I'll use a calculator now...

- jtvatsim

One answer is t = 0.184... the other....

- jtvatsim

t = 3.830

- anonymous

Yes

- jtvatsim

OK, but now what? We have two possibilities either the blocker grabs the ball at t = 0.184 or at t = 3.830... we need a way to figure out which one.

- jtvatsim

But we should at least celebrate our progress so far. YAY!!! :)

- anonymous

Yay !!!!!!!!!!!!! Lol

- jtvatsim

OK, let's do a sanity check with our answers. A useful algebra trick is to plug answers back into the original equations to see if they make sense.

- jtvatsim

Let's not use the -4.9t^2 + ... mess, instead I'll check the other equation:
-1.43t + 4.26

- anonymous

Right Thats Just Makes Us Go To Far.

- jtvatsim

OK, plugging in t = 0.184, I see h = 3.99
But t = 3.830, I see h = -1.22

- jtvatsim

Well, there's a big problem with the second answer. Do you see it? The blocker's hands are a "negative height," in other words he blocks the ball underground. Unless he is a gopher, I think we can conclude that we should go with the first answer t = 0.184

- anonymous

No I Didnt See It , i Just Re-Read The Problem WOW

- anonymous

Almost Missed It

- jtvatsim

Yep, as I mentioned when we first started, this one was a little sneaky. But hopefully that makes sense overall. Any final questions on this one? :)

- anonymous

Yes .

- anonymous

Well I Have A Question Mind Helping With Another Onne ?

- jtvatsim

Go ahead and close this one and post a new one, so it doesn't get too cluttered. See you there! :)

- anonymous

Ok

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