A stone is trown upwards with initial velocity at 20m/s.how long does it take to return to the ground

Answer 1

To find the time it takes for the stone to return to the ground, we can use the kinematic equation:

s = ut + (1/2)at^2

Where:
s = displacement (in this case, the distance covered by the stone)
u = initial velocity (20 m/s)
a = acceleration (in this case, the acceleration due to gravity, which is approximately -9.8 m/s^2) - negative sign indicates direction
t = time

Since the stone is thrown upwards and returns to the ground, its displacement is 0. Therefore, we can rewrite the equation as:

0 = (20)t + (1/2)(-9.8)t^2

Simplifying further:

0 = 20t - 4.9t^2

Rearranging the equation:

4.9t^2 - 20t = 0

Now we can solve for t by factoring out t:

t(4.9t - 20) = 0

From this, we get two solutions:
t = 0 (initial time when stone was thrown)
and
4.9t - 20 = 0

Solving the second equation:

4.9t = 20
t = 20/4.9
t ≈ 4.08 seconds

Therefore, it takes approximately 4.08 seconds for the stone to return to the ground.