Question
A stone is trown upwards with initial velocity at 20m/s.how long does it take to return to the ground
Answers
GPT 3.5
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.
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.