How to calculate time of a falling body with gravity?

we can derive a basic kinematic equation using conservation of energy. consider an object above the ground at a height of "ho". Its total energy is simply the potential energy + kinetic energy provided there is an initial velocity "vo"

E = m*g*ho + ½*m*vo²

now let the object fall from a height "ho" to a final height "h". now the object's total energy is composed of final kinetic energy and potential energy so we arrive at our wanted equation:

m*g*ho + ½*m*vo² = ½*m*v² + m*g*h

now we can simplify it:

g*ho + ½*vo² = ½*v² + g*h

v² = vo² - 2gΔh

where g = 9.8m/s² but we usually use down coordinate to be negative (g = -9.8m/s²) so we can rewrite as

v² = vo² + 2gΔh

now you are given values, just plug them in and solve for the final velocity

v² = 8.9² + 2(-9.8)(-9.8)

v = 16.47 m/s

...

You would have a new Vi (8.9)

Vf^2 = Vi^2 + 2 g d

Vf^2 = 8.9^2 + 2 (9.81) (9.8) = 271.5

Vf = 16.5 m/s

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