Question

The Height , H Of A Baksetball , in meters at t seconds after it is tossed out of a window is modeled by : H=-5t^2 + 20t +15. A Boy Shoots At The Baseball With A Paintball Gun . The Trajectory Of The Paintball Is Given By The Equation : H=3t + 3 . Will The Paintball Hit The Baseball ? IF So When? At What Height Will The Baseball bE ? @jtvatsim

Answer 1

Alrighty, what have we got here...

Answer 2

"something is flying through the air, somebody does something to hit in midair" yep same problem type... :)

Answer 3

Yup Sooo... -5t^2 +20t+15=3t +3

Answer 4

Yessiree! Will the heights be equal? And when? Let's find out. The audience waits in suspense...

Answer 5

Lets Fine Outt Next Step Add ?

Answer 6

Either add or subtract, whatever will make the other side 0. Try something, and I'll let you know what I think. :)

Answer 7

Ok Subtract Because there is only one negative .

Answer 8

You are right to subtract. But not because there is only one negative. Let's pause on this step to make sure you've got this part down. That way, you'll always have the confidence to get through this stage. :)

Answer 9

When I see -5t^2 + 20t + 15 = 3t + 3, I immediately focus my attention on the right side of the equation (look at 3t + 3).

Answer 10

Ok

Answer 11

Then, ask yourself, I see a 3t, how can I get rid of it? In this case I could just subtract a 3t from both sides like this:

-5t^2 + 20t + 15 = 3t + 3
-3t -3t
___________________________
-5t^2 + 17t + 15 = 3

Then my 3t is gone!

Answer 12

But, then, of course, I still see a pesky 3 there. How could I get rid of that since I just want zero on that side? Well... subtract a 3 from both sides, just like we did before!

-5t^2 + 17t + 15 = 3
-3 -3
--------------------
-5t^2 + 17t + 12 = 0

Answer 13

Ohhh i c

Answer 14

Great! It's not too hard once you see the pattern. But it is a little hard to say in words. :)

Answer 15

Here's one more example just to make sure you've got it.

-66t^2 + 24t + 31 = -6t + 4
+6t +6t
---------------------------
-66t^2 + 30t + 31 = 4
-4 -4
----------------------
-66t^2 + 30t + 27 = 0

Answer 16

In this case, I added to get rid of the -6t, but subtracted to get rid of the +4. Any questions on that process?

Answer 17

And of course, what I just wrote above was a made-up example and has nothing to do with "our" current problem. :)

Answer 18

i noticed Lol Those Off #;s

Answer 19

Haha! I tried to make it obvious that I was going crazy there. ;) Anyways, we've got our equation now:
-5t^2 + 17t + 12 = 0

Answer 20

From what I've seen, that should be the end of the "hard" part mathematically. The rest of the problem is just making sure our calculator does the right thing. :)

Answer 21

Yup
Thats The Last Thing 2 do

Answer 22

OK, then. Once you have your proposed solutions from the quadratic formula, we'll compare notes.

Answer 23

Done

Answer 24

Awesome! What did you get?

Answer 25

x1=-0.5
x2 :4

Answer 26

Yep, that's pretty close to what I got,
x1 = -0.59999
x2 = 4

Answer 27

i got the 9999 2 lol

Answer 28

didnt think i needed it

Answer 29

Oh, well, look at you! It's slightly different rounding
-0.59 rounds to -0.6 (then I wouldn't have said anything...)

You can feel that I'm becoming more nit picky! :) That's a good thing, it means you are moving beyond the basics. :)

Answer 30

Lol Im Trying .. Another One Then Ill Leave You Alone Lol

Answer 31

No worries! Glad to help. It's fun watching someone start out struggling, but then learn and start mastering it. It's really cool to see happen. :)

Answer 32

So, we've got our possible solutions, but we need to check them. Here goes...

Answer 33

Looks like t = -0.6 gives h = 1.2
and
t = 4 gives h = 15

Answer 34

The Correct One Is ....4

Answer 35

I'd agree, even though the heights are both positive (and therefore possible), the negative time is weird. The answer is Yes, time is 4, and height is 15. Yahoo! :D

Answer 36

Yay !!!!!!!!!! You Helped Me Sooo Much ..After This Next One Ill Have Just Four More ...Wouldve Been Up All Night

Answer 37

You are welcome! Based on looking at the problems are they relatively similar? If not, I could help you look at one that is a different type if you feel comfortable with these "objects flying and hitting" questions.

Answer 38

This Next One Is A Different One .

Answer 39

Is a summer packet soo

Answer 40

Let's take a look at it then if you want. Even if I have to log off soon, I can at least try to come up with a plan of attack. :)

Answer 41

Sure

Answer 42

sounds good