. A stone is dropped from the top of a building that is 500m high. Disregarding air resistance how long does it take the stone to reach the ground?
Use kinematics equation:
Δx = vi(t) + (1/2)at²
vi=0
g=-9.8
-500=(1/2)(-9.8)t²
t=√(2(-500)/(-9.8))
=10.1 s (approximately)
To find the time it takes for the stone to reach the ground, we can use the equation for free fall motion:
h = (1/2)gt^2
Where:
- h is the height (500m in this case)
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
- t is the time it takes for the stone to reach the ground
By rearranging the formula, we can solve for t:
t = sqrt((2h) / g)
Now, let's substitute the given values:
t = sqrt((2 * 500) / 9.8)
t = sqrt(1000 / 9.8)
t ≈ sqrt(102.04)
t ≈ 10.1 seconds
So, disregarding air resistance, it takes approximately 10.1 seconds for the stone to reach the ground.