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 ?

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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 ?

Mathematics
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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.
yes
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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Other answers:

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:
-4.9t^2 + 19.67t +5.06 = 0 Do you see how I got that?
Umm I Think So
Adding Correcct? 1.43 + 4.26 TO BOTH SIDES
Oh wait, lol. Good catch. I was supposed to add the 1.43t, but subtract the 4.26. Sorry about that. :)
-4.9t^2 + 19.67t - 3.46 = 0 There... that's better. :P
That should make more sense now. OK so far?
YES
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?
i Remember
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. :)
What we can definitely say is that: a = -4.9 b = 19.67 and c = -3.46 for when we plug in.
\[\frac{-b\pm\sqrt{b^2-4ac}}{2a} = \frac{-19.67\pm\sqrt{19.67^2-4(-4.9)(-3.46)}}{2\cdot -4.9}\]
Exactly Correct
Perfect! Now to simplify that horrid looking nightmare. I'll use a calculator now...
One answer is t = 0.184... the other....
t = 3.830
Yes
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.
But we should at least celebrate our progress so far. YAY!!! :)
Yay !!!!!!!!!!!!! Lol
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.
Let's not use the -4.9t^2 + ... mess, instead I'll check the other equation: -1.43t + 4.26
Right Thats Just Makes Us Go To Far.
OK, plugging in t = 0.184, I see h = 3.99 But t = 3.830, I see h = -1.22
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
No I Didnt See It , i Just Re-Read The Problem WOW
Almost Missed It
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? :)
Yes .
Well I Have A Question Mind Helping With Another Onne ?
Go ahead and close this one and post a new one, so it doesn't get too cluttered. See you there! :)
Ok

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