A stone is trown upwards with initial velocity at 20m/s.how long does it take to return to the ground
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.
To find out how long it takes for the stone to return to the ground, we can use the kinematic equation for vertical motion:
h = h0 + v0*t - 0.5*g*t^2
Where:
h = final height (in this case, 0 since it returns to the ground)
h0 = initial height (which we can assume to be 0)
v0 = initial velocity (20 m/s upward)
g = acceleration due to gravity (approximately 9.8 m/s^2)
t = time
Plugging in the values, we can solve for t:
0 = 0 + 20*t - 0.5*9.8*t^2
0 = 20t - 4.9t^2
Rearranging the equation, we get:
4.9t^2 - 20t = 0
Now, we can factor out t:
t(4.9t - 20) = 0
Setting each factor equal to zero:
t = 0 (which means it took 0 seconds to reach the ground initially)
4.9t - 20 = 0
Using the quadratic formula, we can solve for t:
t = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 4.9, b = -20, and c = 0. Plugging in the values:
t = (-(-20) ± √((-20)^2 - 4(4.9)(0))) / (2(4.9))
t = (20 ± √(400 - 0)) / 9.8
t = (20 ± √400) / 9.8
t = (20 ± 20) / 9.8
Simplifying further:
t = (20 + 20) / 9.8 = 40 / 9.8 ≈ 4.08 seconds
t = (20 - 20) / 9.8 = 0 / 9.8 = 0 seconds
Since time cannot be negative, the only meaningful solution is t = 4.08 seconds. Therefore, it takes approximately 4.08 seconds for the stone to return to the ground.