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

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