Isolating t in horizontal motion equation

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To isolate "t" in the horizontal motion equation, start with the formula d = ½at². For a flowerpot falling from 18m, set up the equation as 18m = ½(9.8m/s²)t². Multiply both sides by 2 to eliminate the fraction, resulting in 36 = 9.8t². Divide by 9.8 to solve for t², yielding t² = 3.67, and then take the square root to find t ≈ 1.91 seconds. This process clarifies how to isolate "t" in motion equations.
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Isolating "t" in horizontal motion equation

Homework Statement


So this is just a practice question from my course and they gave me the answer, the problem I am having is understanding how they got to that answer. I have the formula and everything, just don't know how to isolate "t" and the steps to do so


-How long does it take for a flowerpot to fall from a balcony that is 18m above the ground?


Homework Equations



d=½a\nablat²

The Attempt at a Solution



18m [down] = ½(9.8m/s²)\nablat²
and I know I have to isolate the "t" but how do I go about doing that, I keep getting it wrong

The answer is 1.9s,
 
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After posting this, I sat for another 2 hrs trying to figure out the problem and I finally understood it.

18m [down] = ½(9.8m/s²)∇t²
18(2)=9.8(t²)
36=9.8(t²)
36/9.8 = t²
3.67=t²
squareroot 3.67 = t
1.91=t
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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