/sci/ - Science & Math

Question regarding particle motion relating to gravity, I just don't know what I'm doing wrong here.

Basically something on a spring pulled back at length 2cm launches itself, a 100g object, into the air. 60cm is its apex. I'm trying to find the spring constant (Force of spring = constant * length pulled back) or time. I can't seem to set myself up a proper equation to solve this. Anyways, here's what I've done:

initial velocity + velocity of gravity *t= 0
1/2 -k x^2 -9.8t = 0
differentiate
1/6 -k x^3 - 4.9t^2 = .6
now I solve for k
-kx^3 - 29.4t^2 = 3.6
-k(.02^3) - 29.4t^2 = 3.6
-k(.000008) - 29.4t^2 = 3.6
-k - 3675000t^2 = 450000
-k = 450000 + 3675000t^2

Now I plug this into my equation for velocity (I just solved for k in regards to position)
1/2 -kx^2 - 9.8t = 0
1/2 (450000 + 3675000t^2)(.02^2) - 9.8t = 0
1/2 (180 + 1470t^2) - 9.8t = 0
90 + 735t^2 - 9.8t = 0
Now it's in the form of a quadratic:
735t^2 - 9.8t + 90 = 0
Not even gonna think about factoring that, just gonna put it into the quadratic formula
ax^2 + bx + c x = (-b +- sqrt(b^2-4ac))/(2a)
t = (9.8 +- sqrt(96.04 - 4(735)90)/(1470)
t = (9.8 +- sqrt(96.04 - 264600))/(1470)
t = (9.8 +- sqrt(-264503.96))/1470)
t = 524.1i / 1470
t = .357i
I don't really know what to do with the i here :X substituting this shit back into my equation:
1/2 -kx^2 - 9.8t = 0
-k *.0002 - 9.8(.357) = 0
-k = 3.4986 / .0002
-k = 17493N

which is very different from the given answer of 2940N (their answer doesn't provide an explanation ofc)

So where'd I go wrong?

"Chance" is the quotient of the number of desired (or in this case, investigated) outcomes divided by the number of possible outcomes.

Possibility it's a boy: 1/2
Possibility it's ALSO a boy: 1/3

Note the "a" or "also". This is interpretation of speech, not arguable mathematical processes.

So all this comes down to is whether you want to know the gender of the one child to be, or the possibility for the two children to have been male. Stop arguing this /sci/.