How high is a building when an anvil takes 4 seconds to hit the ground?
How long will it take a piano to hit the ground when dropped off a building 103 meters high?
a. h = 0.5g*t^2 = 4.9*4^2 = 78.4 m
b. h = 0.5g*t^2
h = 103 m.
g = 9.8 m/s^2
Solve for t.
To determine the height of the building when an anvil takes 4 seconds to hit the ground, we can use the equation of motion:
h = (1/2) * g * t^2
Where:
h = height of the building
g = acceleration due to gravity (approximated as 9.8 m/s^2)
t = time taken for the object to fall (in this case, 4 seconds)
Plugging in the values:
h = (1/2) * 9.8 * 4^2
h = (1/2) * 9.8 * 16
h = 78.4 meters
Therefore, the height of the building is approximately 78.4 meters.
Now, to calculate the time it will take for a piano to hit the ground when dropped off a building 103 meters high, we can use the same equation of motion:
h = (1/2) * g * t^2
Rearranging the equation to solve for t:
t = sqrt(2h / g)
Plugging in the values:
t = sqrt(2 * 103 / 9.8)
t = sqrt(206 / 9.8)
t ≈ sqrt(21.02)
t ≈ 4.58 seconds
Therefore, it will take approximately 4.58 seconds for the piano to hit the ground when dropped from a building 103 meters high.
To determine the height of a building when an object takes a certain time to fall, we can use the equations of motion. One of the most common equations is:
h = (1/2) * g * t^2
where h is the height, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time it takes for the object to fall.
Let's first calculate the height of the building when an anvil takes 4 seconds to hit the ground.
Using the equation, we rearrange it to solve for h:
h = (1/2) * g * t^2
h = (1/2) * 9.8 m/s^2 * (4 s)^2
h = (1/2) * 9.8 m/s^2 * 16 s^2
h = 78.4 meters
Therefore, the building is approximately 78.4 meters high when an anvil takes 4 seconds to hit the ground.
Now, let's calculate how long it will take a piano to hit the ground when dropped off a building that is 103 meters high.
Rearranging the equation to solve for t:
h = (1/2) * g * t^2
103 m = (1/2) * 9.8 m/s^2 * t^2
103 m = 4.9 m/s^2 * t^2
t^2 = 103 m / 4.9 m/s^2
t^2 = 21.02 s
t ≈ √21.02 s
t ≈ 4.59 s
Therefore, it will take approximately 4.59 seconds for the piano to hit the ground when dropped off a 103-meter high building.