A stone is dropped from the top of a cliff. It hits the ground below after 3.10 s. How high is the cliff?
If H is the distance fallen in time t,
H = (g/2) t^2
Set t = 3.10 s and solve for H.
g is the acceleration of gravity, 9.8 m/s^2
3.10 x 9.8=30.38
30.38^2=922.9444
922.9444/9.8^2
922.9444/19.6= 47.0m
To calculate the height of the cliff, we can use the formula for the distance traveled by an object in free fall:
d = (1/2) * g * t^2
Where:
d = distance traveled (height of the cliff)
g = acceleration due to gravity (approximately 9.8 m/s^2)
t = time taken to reach the ground (3.10 s in this case)
Plugging in the values, we have:
d = (1/2) * 9.8 * (3.10)^2
d = 4.9 * 9.61
d = 46.99 m
Therefore, the height of the cliff is approximately 46.99 meters.
To find the height of the cliff, we can use the formula for the distance fallen by an object under the influence of gravity:
h = (1/2) * g * t^2
Where:
h = height of the cliff
g = acceleration due to gravity (approximately 9.8 m/s^2)
t = time taken for the stone to hit the ground (3.10 s)
Plugging in the values into the formula:
h = (1/2) * 9.8 * (3.10)^2
h = 15.19 meters
Therefore, the height of the cliff is approximately 15.19 meters.