Question

how do you isolate t (time) in this equation? the question is asking me to derive an equation for time to hit the ground for a dropped object in terms of height of the drop, gravity, and initial velocity and that’s what i have so far.

Answer 1

Fine, so we have the equation

S = So + Vo.t + at²/2

We have the final height = 0 and since its dropped, Vo = 0, our a will be the gravity, negative since its falling

0 = So + 0.t - gt²/2

0 = So - gt²/2

Since So is our h, lets change the letter

0 = h - gt²/2

gt²/2 = h

gt² = 2h

t² = 2h/g

t = $\sqrt{\frac{2h}{g}}$