Question

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 ?

Answer 1

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.

Answer 2

yes

Answer 3

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

Answer 4

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:

Answer 5

-4.9t^2 + 19.67t +5.06 = 0

Do you see how I got that?

Answer 6

Umm I Think So

Answer 7

Adding Correcct? 1.43 + 4.26 TO BOTH SIDES

Answer 8

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

Answer 9

-4.9t^2 + 19.67t - 3.46 = 0

There... that's better. :P

Answer 10

That should make more sense now. OK so far?

Answer 11

YES

Answer 12

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?

Answer 13

i Remember

Answer 14

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. :)

Answer 15

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

Answer 16

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

Answer 17

Exactly Correct

Answer 18

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

Answer 19

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

Answer 20

t = 3.830

Answer 21

Yes

Answer 22

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.

Answer 23

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

Answer 24

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

Answer 25

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.

Answer 26

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

-1.43t + 4.26

Answer 27

Right Thats Just Makes Us Go To Far.

Answer 28

OK, plugging in t = 0.184, I see h = 3.99

But t = 3.830, I see h = -1.22

Answer 29

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

Answer 30

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

Answer 31

Almost Missed It

Answer 32

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? :)

Answer 33

Yes .

Answer 34

Well I Have A Question Mind Helping With Another Onne ?

Answer 35

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

Answer 36

Ok