a stone is dropped from the top of a cliff. it is seen to hit the ground 3.5 seconds later. how high is the cliff
To determine the height of the cliff, we can use the formula for distance traveled by a falling object:
distance = (1/2) * acceleration due to gravity * time^2
The acceleration due to gravity is approximately 9.8 m/s^2.
Let's substitute the given values into the formula:
time = 3.5 seconds
acceleration due to gravity = 9.8 m/s^2
distance = (1/2) * 9.8 * (3.5)^2
Calculating this expression will give us the height of the cliff. Let's do the math:
distance = (1/2) * 9.8 * 12.25
distance = 4.9 * 12.25
distance = 59.725
Therefore, the height of the cliff is approximately 59.725 meters.
To calculate the height of the cliff, we can use the equation for free fall motion:
h = (1/2) * g * t^2
Where:
h = height of the cliff
g = acceleration due to gravity (approximately 9.8 m/s^2 on Earth)
t = time taken for the stone to hit the ground (in seconds)
In this case, the stone takes 3.5 seconds to hit the ground. Plugging this value into the equation, we get:
h = (1/2) * 9.8 * (3.5)^2
= (1/2) * 9.8 * 12.25
= 4.9 * 12.25
= 59.725
Therefore, the height of the cliff is approximately 59.725 meters.