Question

Two Cirque Du Soleil Performers Are Launched Toward Each Other From Two Slightly Offset Seesaws The First Performer Is Launched And One Second later , The Second Performer Is Launched in other Direction .They Both Performed A Flip And gave a high five in the air each performer is in the air for 2 seconds . The Height above the seasaw (h) at any given time (t) is approximated by parabolas
h=-5(t-1)^2 +5
h=-5 ( t-2)^2 +5
determine the height of the performers when they ''high fived '' @jvatsim

Answer 1

Hmm... interesting. I see that the second equation is just as nasty as the first one (the only difference is a t-1 vs. a t-2). But I bet the big picture idea is still the same. :)
1) Set equal
2) Solve for t
3) Check answer.

Answer 2

This One Is Tricky .

Answer 3

Yeah, I notice that on the surface we also have a weird (t-1)^2 and (t-2)^2 expansion needed too. We have to "expand the binomial" in math speak.

Answer 4

Ok.

Answer 5

Let's try it and see what we get. We'll start with the first equation
-5(t-1)^2 + 5

Answer 6

Alright, well I don't like the whole parenthesis squared thing so let's remember that exponents just mean to multiply the same thing twice:

-5(t-1)^2 + 5 --> -5(t-1)(t-1) + 5

Answer 7

Does that make sense so far?

Answer 8

Kind Of

Answer 9

Alright, keep track of what you are thinking and what is confusing. Let me finish the full thought here and see if that helps. :)

Answer 10

We rewrite:
-5(t-1)^2 + 5 -> -5(t-1)(t-1) + 5
then, we use FOIL or distribution (whichever you learned) to get:
-5(t-1)(t-1) + 5 -> -5( t^2 - t - t + 1) + 5
simplifying:
-5(t^2 - t - t + 1) + 5 -> -5(t^2 - 2t + 1) + 5
distribute the -5 (watch out for sign changes!):
-5(t^2 - 2t + 1) + 5 -> -5t^2 + 10t - 5 + 5
simplifying:
-5t^2 + 10t - 5 + 5 -> -5t^2 + 10t

I know that is a lot, but see if you can follow the thought process. If you have any questions, I'll be happy to try and answer them. There are several algebra ideas floating around here.

Answer 11

Look Like Something I Seen Before

Answer 12

That's a good thing... I suppose. When it comes to math, we're basically saying "Yep, I've seen Godzilla before." :)

Answer 13

Lol Right .

Answer 14

Ahh! Error.... Here it is corrected. :)

Well, if you are brave, we can do the same thing with the other equation -5(t-2)^2 + 5.

If we do it carefully, we get
-5(t-2)^2 + 5
-5(t-2)(t-2) + 5
-5(t^2 - 2t - 2t + 4) + 5
-5(t^2 - 4t + 4) + 5
-5t^2 + 20t - 20 + 5
-5t^2 + 20t - 15

Yikes... but, OK. :P Should have been -15 at the end.

Answer 15

ok got it

Answer 16

Is there any step in particular that is confusing? Hopefully most of the make sense.
The concepts here (in case you remember the names, which I never did):

expand binomial: (t-1)^2 = (t-1)(t-1)
FOIL: (t-1)(t-1) = first + outer + inner + last = t*t + t*-1 + -1*t + -1*-1 = t^2 -t -t + 1 = t^2 - 2t + 1

Answer 17

Oh, well you said you got it, but just checking... :)

Answer 18

i was saying i got the 1st step lol but the whole binomial never heard of it

Answer 19

No worries, you may have heard it called something different. Terminology is replaceable. :)

Answer 20

i heard of terminology

Answer 21

Well, now we are actually through most the hard part of this question.
1) Expand the equations we got
-5(t-1)^2 + 5 ---> -5t^2 + 10t
and
-5(t-2)^2 + 5 ---> -5t^2 + 20t - 15

All we do now is set these two equations equal to each other, and proceed as before.

Answer 22

soooo -5t^2 +10t=-5t^2 + 20t - 15

Answer 23

Right! Now, we can choose to move one side or the other it doesn't matter. I'll move the left side since it is shorter (less steps). :)

Answer 24

-5t^2 + 10t = -5t^2 + 20t - 15
+5t^2 +5t^2
------------------------
10t = 20t - 15

ooooh nice, the t^2's are gone!

10t = 20t - 15
-10t -10t
-------------
0 = 10t - 15

I don't like it written backwards, so I will spin it around

10t - 15 = 0

There. We don't even need the quadratic formula for this one!

Answer 25

yay this one was fun
but different

Answer 26

Yes, the mathematical definition of "fun" is "utterly tortuous and ridiculous". :) If you get into math at the master's level the definition of an "interesting problem" is one that "you have no clue how to solve". lol

Answer 27

Just to finish it off (though I'm sure you already finished the missing steps)... 10t = 15, so t = 15/10 = 1.5.

Answer 28

very ..

Answer 29

I've got to head out now. But I do want to give you a link to a very good resource: Check out desmos.com It is a very powerful graphing calculator that lets you "see" the answer visually. It is not a replacement for knowing the algebra (in class you still need to solve it manually), but I think it is cool to know that there is technology that does these problems instantly. :)

For example, I did this problem we just solved: https://www.desmos.com/calculator/1h08m4ibe7

Answer 30

thanks , ill stay in touch your awesome

Answer 31

Of course, whoever wrote the code for the computer needed to know the handwritten algebra first... :)

Thanks! I hope you got something out of all the crazy math notation I threw at you. It's still weird that little symbols allow us to communicate ideas... crazy stuff... Take care! :)