Algebra Help!! D:

hedwig68 • 13 March 2013 at 7:03 PM

Yeah, I'm having some trouble with this one word problem. Here is is:

A diver is standing on a platform 24 ft above the pool. He jumps from the platform wih an initial upward velocity of 8 ft/s. Use the formula h= -16t+vt+s, where h is his height above the water, t is the time, v is his starting upward velocity, and s is his startin height. How long will it take for him to hit the water?

Also, explain how you got the answer so I can learn how to do it my self. ^^

Help?

twilight_raptor • 13 March 2013 at 7:57 PM

@hedwig68

(solving for t)

h= -16t + vt + s

(start plugging in what you know)

24 = -16t + 8t +24
24 -24 = -8t +24 -24
0= 8t (no thats wrong Dx are you sure about the equation?)

hey I'm not familiar with that equation so let me use some equations that I know:
(a= acceleration of gravity = 32.2 ft/s)
First we will calculate (1) how long it takes him to reach his max height. Then add that time to (2) how long it takes him to fall k

(1)
at = final velocity - initial v
t = (final v - initial v)/a
t= (0-8)/-32.2
t= 24.2 s

We will need his height above ground for the next part so:
h= initial v t + 1/2 at^2
h= 8(24.2) + 16.1 (24.2^2)
h= 193.6 + 9428.8
h= 9622 ft above his platform
height above ground= 9622 + 24= 9646.4

(2)
h= initial v t + 1/2 at^2
9646.4 = 0t + 1/2 32.2 (t^2)
9646.4= 16.1 t^2
9646.4/16.1 =t^2
599.2 = t^2
[square root] 599.2 =t
24.5s =t

therefore total time =24.5 + 24.2 = 48.7s
(do you have an answer sheet to check this answer because I'm not sure...)

hedwig68 • 13 March 2013 at 8:13 PM

@twlight_raptor

I'm really confused still, I'm not really sure what all of those eqations mean. O.O' And yes, I am positive that's the right equation and no, I don't have an answer sheet.

trish • 13 March 2013 at 8:28 PM

@hedwig68 I learned this about a month ago. 😊 Almost exact problem.

h= -16t+vt+s
v=velocity=8
s=starting height=24

Plug in the numbers.
h=-16t+8t+24

Now we are going to use the Zero Property thingie-which-I-forgot-how-its-called. So h will be 0. Leaving one variable.

-16t+8t+24=0
Wait. Did you copy down the problem wrong? It's supposed to be -16t SQUARED?

-16t^2+8t+24=0
Backwards distribute (Factoring)

8(-2t^2+t+3)=0

Forget the 8 now.

-2t^2+t+3
Continue factoring. Have you learned the Diamond strategy yet? It's not something I can show typing. But I can take a picture for you of how to do this.

hedwig68 • 13 March 2013 at 8:49 PM

@trish

*facepalm* Yeah, I meant -16t squared. XD

And I get what you're saying, by doing all that. ^^ Also, I don't know the diamond strategy. I know the box strategy though, maybe they are allike. ^^

trish • 13 March 2013 at 8:52 PM

@hedwig68 Still need help? The diamond is the step before the box, the way I was taught. 😋

hedwig68 • 13 March 2013 at 8:56 PM

@trish

Yeah, just a tiny bit, I'm eginning to understand though. ^^ So what happens next, this is where I usually do grouping. 😋 Or is that what you do?

trish • 13 March 2013 at 9:18 PM

@hedwig68

It's a quadratic.
-2t^2+t+3

Multiply the A term (-2t^2) and the C Term (3) together, making -6t^2. Now you have to find two numbers that add up to the B term (1t) but also multiplied, will make the new A Term (-6t^2).

The Answer to that ^^? 3t & -2t.
3t + -2t = 1t = B Term
(3t)(-2t)= -6t - A Term.

Now box it.
In top box left, write -2t^2. Top right, is 3t. Bottom left, is -2t. Bottom right, is 3.

Find the two pairs of equations that make it. You know this part?

(-2t+3) and (t+1)
now..
-2t+3=0 and t+1=0
MAKE them equal zero.

-2t+3=0
Subtract 3 form left side and do it to the right side.
-2t=-3
Divide by -2.
Equals 3/2.

And do the same to t+1=0
t+1=0
t=-1

Quadratics have two answers.
T= 3/2 and -1.
Now, only ONE of them make sense. You can't have a negative time for the original problem, so your final answer to the word problem is 3/2.

Get it? If you don't, tell me which step gets you stumped.

hedwig68 • 13 March 2013 at 10:03 PM

@trish

Actuslly I understand that part, we learned the first part last week and the last part this week. I just didn't know how to fit it all together and make it eqwual that. You really helped with that though, thanks a lot! I completely understand now! 😊

trish • 13 March 2013 at 10:06 PM

@hedwig68 You're welcome, I love algebra. 😊