Neglect air resistance and determine the height of the school.?

Question

A pebble rolls off the roof of the school and falls vertically. Just before it reaches the ground, the pebble's speed is 17 m/s. Neglect air resistance and determine the height of the school.

Answer 1

d = 1/2 at^2
v = at
t = v/a

d= 1/2 a (v/a)^2
d = 1/2v^2/a = 1/2*(17^2)/(9.8) = 14.75 meters

Answer 2

you could additionally use another of newton's equations:
v^2 = u^2 + 2as
where v is the final velocity, u is the initial velocity, a is the acceleration of the pebble. in this case, the acceleration is caused due to gravity and so, we can consider it to be the constant, g=9.8m/s^2
also, since the pebble was dropped from rest, the initial velocity, u is 0.
putting all these inputs in the equation,
17*17 = 2*9.8*s
s = 14.74 m

Answer 3

Two ways to do this one:

(1) Use laws of motion

v = g t
and
h = ½ g t²

Using the first equation you can calculate the time. Then plug the time into the second equation to get the height h.

(2) Equate kinetic energy to potental energy

½ m v² = m g h

h = ½ v² / g

Answer 4

1/2mv^2=mgh
1/2(17)^2/9.8=h
h=14.74 m