final velocity of a falling object = 0
and acceleration of a falling object is negative
now using the expression ( Newton's 3rd equation of motion)
[tex] {v}^{2} = {u}^{2} - 2gs[/tex]
where the parameters have their usual meaning
making
[tex] {u}^{2} \: the \: subject[/tex]
thus
[tex] {u}^{2} = 2gs[/tex]
[tex]u = \sqrt{2gs} [/tex]
from the question,
g= 9.8m/s^2
s = 30m
substitute them into the equation
[tex]u = \sqrt{2(9.8 \times 30)} [/tex]
[tex]u = \sqrt{588} [/tex]
u = 24.25m/s
but the question is demanding for time but not the initial velocity
so substitute them in the
Newton's first equation of motion
where
V = u - gt
but from the question,
v= 0 and the acceleration is negative because it's a free fall
substitute the values into the equation
0 = 24.24 -9.8t
making t the subject
9.8t = 22.24
dividing through by 9.8
9.8t/9.8 = 22.24/9.8
t = 2.3s . therefore, it would take 2.3s for the ball to hit the ground.
