galileo drops a stone from the tower of pisa which is 45m high. at what speed does the stone hit the ground
30m/s
To determine the speed at which the stone hits the ground, we can use the equations of motion. We know that the stone is dropped from rest and falls freely under the influence of gravity.
The equation that relates the height, gravitational acceleration, and velocity of a freely falling object is:
v^2 = u^2 + 2as
Where:
v = final velocity (speed at which the stone hits the ground)
u = initial velocity (which is zero in this case as the stone is dropped)
a = acceleration due to gravity (approximately 9.8 m/s^2)
s = distance or height fallen (45 m in this case)
Substituting the known values into the equation, we have:
v^2 = 0 + 2(9.8)(45)
v^2 = 2(9.8)(45)
v^2 = 2(441)
v^2 = 882
v ≈ √882
v ≈ 29.699 m/s
Therefore, the approximate speed at which the stone hits the ground is 29.699 m/s.
To calculate the speed at which the stone hits the ground when dropped from a height, we can use a basic physics formula.
The formula to calculate the speed (v) at which an object falls due to gravity is:
v = √(2 * g * h)
where:
v = speed (in meters per second)
g = acceleration due to gravity (9.8 m/s^2 on Earth)
h = height (in meters)
Using this formula, let's calculate the speed at which the stone hits the ground when dropped from a height of 45 meters:
v = √(2 * 9.8 * 45)
v = √(882)
v ≈ 29.7 m/s
Therefore, the stone hits the ground with a speed of approximately 29.7 meters per second.