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.
thanks in advance,
Euph.
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?
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...
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...
[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.
*******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!