a stone dropped from the roof at a velocity of 6m/s2 and reaches the ground with the velocity of 18m/s.how high is the roof from the ground

use

v1²-v0²=2gS
where S is the height of the roof, g=acceleration due to gravity, v0 and v1 are initial and final velocities.

6 m/s^2 is not a velocity. You must have meant 6 m/s.

mathmate is correct. The answer will not depend upon the angle that the stone was thrown. The time the stone is in the air WILL depend upon that angle.

To find the height of the roof, we can use the principles of physics and the equations of motion.

First, we need to calculate the time taken for the stone to reach the ground. We can use the equation:

v = u + at

Where:
v = final velocity (18 m/s)
u = initial velocity (6 m/s)
a = acceleration due to gravity (approximately 9.8 m/s²)
t = time taken

Rearranging the equation, we have:

t = (v - u) / a

Substituting the given values, we get:

t = (18 - 6) / 9.8
t ≈ 1.22 seconds

Since we now know the time it took for the stone to fall, we can calculate the height of the roof using the equation:

s = ut + (1/2)at²

Where:
s = height of the roof (unknown)
u = initial velocity (6 m/s)
t = time taken (1.22 seconds)
a = acceleration due to gravity (approximately 9.8 m/s²)

Plugging in the values, we have:

s = (6 * 1.22) + (0.5 * 9.8 * 1.22²)
s ≈ 7.32 + 7.17
s ≈ 14.49 meters

Therefore, the height of the roof from the ground is approximately 14.49 meters.