What is the simplest formula for determining the time taken to hit the ground for an object dropped from a known height?

Question

What is the simplest formula for determining the time taken to hit the ground for an object dropped from a known height?

g is 10, initial velocity is 0 and air resistance is negligible

Answer 1

The simplest formula if you know the height y_o is y = -1/2 gt² + V_ot + y_o where V_o is initial velocity =0 ,

and y_o is initial height. When the object hits the ground, y or final height is = 0

Incorporating all this info into the equation, 0 = -1/2 gt² + 0 + y_o , and -y_o = -1/2 gt² , y_o = 1/2 gt² ,

rearranging 2y_o = gt², t² = 2y_o /g , t = √(2y_o/g) , t = √(2y_o/ 10 m/s²)

Since we do not know the initial height y_o lets at least check the units

if y_o is known then the units become m / (m/s²), or (m.s²/ m) When m cancels out you are left with s² under the radical and the sqrt of that is s which is the time unit. Therefore the simplest form to find the time is

t = √(2y_o / 10 m/s²)