given:

1. s= (-1/2)gt^2 + 10t + 2

and

2. v = 10 - gt

i want to eliminate the t term to give:

v^2 = 4g + 100 - 2gs

i'm really struggling with this one.. i rearrange eq.2 for t: giving:

t = v + 10 / (-g)

subbing this into eq. 1. i'm a little overwhelmed where to start.. appreciate any help.

Euph.

Originally Posted by euphmorning
given:

1. s= (-1/2)gt^2 + 10t + 2

and

2. v = 10 - gt

i want to eliminate the t term to give:

v^2 = 4g + 100 - 2gs

i'm really struggling with this one.. i rearrange eq.2 for t: giving:

t = v + 10 / (-g) <--- that should be: t = (10-v)/g

subbing this into eq. 1. i'm a little overwhelmed where to start.. appreciate any help.

Euph.
Substituting t by the term (10-v)/g yields:

$s = -\frac12 \cdot g \cdot \left(\frac{10-v}{g} \right)^2+10\left(\frac{10-v}{g} \right)+2$

Expand the brackets and collect like terms. Afterwards you can factor the numerator.

You should come out with:

$s = \frac{(v+10)(v-10)}{2g}+2$

thankyou for your informed reply. unfortunately i'm still a little stuck. evidently i really need to go over my algebra.. is there any chance of a work through what is going on to get this factorised as given, then rearrangment to v^2?

Do you realise that (v + 10)(v - 10) = v^2 - 100 ?
If not, then you are unaware of basics, so need classroom help...

Yes, i perfectly reason that Wilmer. That is not the problem i'm having. as i've stated, it's arriving at that which i'm having difficultly with.

Well, to start, do you agree that your t = v + 10 / (-g) is incorrect and should be: t = (10-v) / g;
PLUS that you needed brackets with yours: t = (v + 10) / (-g) ?

I'm not sure about Earboth's s = (v + 10)(v - 10) / (2g) + 2:
that simplifies to v^2 = -4g + 100 + 2gs, NOT to v^2 = 4g + 100 - 2gs as in your initial post...
did you make a typo? Maybe we'll wait to see what Earboth has to say...

Originally Posted by earboth
$s = \frac{(v+10)(v-10)}{2g}+2$
Had another look...above is incorrect (sorry Earboth!); should be:
s = 2 - (v+10)(v-10) / 2g
This leads to your v^2 = 4g + 100 - 2gs : so you made no typo!

You want help in getting to above, right? Well, let's see:

s = -g/2[(10-v)/g]^2 + 10[(10-v)/g] + 2 : that's what we start with, ok?
Multiply by -2:
-2s = g[(10-v)/g]^2 - 20[(10-v)/g] - 4 : changes -g/2 to g (easier!)
Expand:
-2s = g[(100 - 20v + v^2) / g^2] - (200 + 20v) / g - 4
Multiply by g:
-2gs = 100 - 20v + v^2 - 200 + 20v - 4g
Simplify:
-2gs = v^2 - 100 - 4g
In terms of v^2:
v^2 = 4g + 100 - 2gs : SUCCESS!!

By the way, that was my way of doing it; there are other ways...

Wilmer, Brilliant - exactly what I needed help with. Thanks!

kind regards,

Euph.

Here is what I did ... (if I've made amistake I apologize for the confusion!)
Originally Posted by earboth
Substituting t by the term (10-v)/g yields:

$s = -\frac12 \cdot g \cdot \left(\frac{10-v}{g} \right)^2+10\left(\frac{10-v}{g} \right)+2$

...
Originally Posted by Wilmer
Well, to start, do you agree that your t = v + 10 / (-g) is incorrect and should be: t = (10-v) / g;
PLUS that you needed brackets with yours: t = (v + 10) / (-g) ?

I'm not sure about Earboth's s = (v + 10)(v - 10) / (2g) + 2:
that simplifies to v^2 = -4g + 100 + 2gs, NOT to v^2 = 4g + 100 - 2gs as in your initial post...
did you make a typo? Maybe we'll wait to see what Earboth has to say...
My re-arrangerments of the equation above:

$s = - \left(\frac{10-v}{2g} \right)^2+20\left(\frac{10-v}{2g} \right)+2$

Factoring out $\frac{10-v}{2g}$ :

$s = \left(\frac{10-v}{2g} \right)(-(10-v)+20)+2$

$s = \left(\frac{10-v}{2g} \right)(10+v)+2$

I can't detect a mistake ... so sorry.

Originally Posted by Wilmer
Had another look...above is incorrect (sorry Earboth!); should be:
s = 2 - (v+10)(v-10) / 2g
This leads to your v^2 = 4g + 100 - 2gs : so you made no typo!

You want help in getting to above, right? Well, let's see:

s = -g/2[(10-v)/g]^2 + 10[(10-v)/g] + 2 : that's what we start with, ok?
Multiply by -2:
-2s = g[(10-v)/g]^2 - 20[(10-v)/g] - 4 : changes -g/2 to g (easier!)
Expand:
-2s = g[(100 - 20v + v^2) / g^2] - (200 + 20v) / g - 4 <--- are you sure?
Multiply by g:
-2gs = 100 - 20v + v^2 - 200 + 20v - 4g
Simplify:
-2gs = v^2 - 100 - 4g
In terms of v^2:
v^2 = 4g + 100 - 2gs : SUCCESS!!

By the way, that was my way of doing it; there are other ways...
...

[Earboth]:
-2s = g[(10-v)/g]^2 - 20[(10-v)/g] - 4 : changes -g/2 to g (easier!)
Expand:
-2s = g[(100 - 20v + v^2) / g^2] - (200 + 20v) / g - 4 <--- are you sure?
.................................................. .................................................. ....................................

Whoops....typo: should be (200 - 20v)
-2s = g[(100 - 20v + v^2) / g^2] - (200 - 20v) / g - 4 <--- are you sure?
You can tell by the line that follows above:
2gs = 100 - 20v + v^2 - 200 + 20v - 4g

OK?!
Btw, yes, I am SURE of final result: tested it.

Originally Posted by earboth
$s = - \left(\frac{10-v}{2g} \right)^2+20\left(\frac{10-v}{2g} \right)+2$ *******1

Factoring out $\frac{10-v}{2g}$ :

$s = \left(\frac{10-v}{2g} \right)(-(10-v)+20)+2$

$s = \left(\frac{10-v}{2g} \right)(10+v)+2$ *******2

I can't detect a mistake ... so sorry.
*******1, *******2 : those 2 do not equate; try v=2 and g=2 :
*******1: s = 38
*******2: s = 26

I think your mistake is going from (-g/2)[(10-v)/g]^2 to -[(10-v)/(2g)]^2

The initial equation given by the OP is : s= (-1/2)gt^2 + 10t + 2
I think the best/easiest way to START is divide through by (-1/2)g = -g/2:
-2s/g = t^2 - 20t/g - 4/g
Then ambiguosities have vanished!