Question

If a stone takes 6.39 seconds to fall from a 200 meter cliff, how high of a cliff will a stone take 12.76 second to fall from?

Answer 1

To calculate the height of a cliff when it takes a stone 12.76 seconds to fall, we can use the formula for the distance fallen by an object. Plugging in the values, we find that the stone will take 12.76 seconds to fall from a 776.44 meter cliff.

Step-by-step explanation:

To calculate the height of a cliff when it takes a stone 12.76 seconds to fall, we can use the formula for the distance fallen by an object:

d = (1/2) * g * t^2

Where d is the distance fallen, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time of fall. Rearranging the formula to solve for d gives:

d = (1/2) * g * t^2

We can plug in the values to find the height of the cliff:

d = (1/2) * 9.8 * 12.76^2 = 776.44 meters

Therefore, the stone will take 12.76 seconds to fall from a 776.44 meter cliff.

Answer 2

We know that in a free fall the distance is given by:

`y=(1)/(2)gt^2`

In this case we know that the distance in the first fall is 200 m and that it takes 6.38 seconds to travel this distance then we have that the gravity is:

`\begin{gathered} 200=(1)/(2)(6.38^2)g \\ g=(400)/(6.38^2) \end{gathered}`

Once we know the value of the gravity for the first fall we can calculate the distance travel in the second fall:

`\begin{gathered} y=(1)/(2)((400)/(6.38^2))(12.76)^2 \\ y=800 \end{gathered}`

Therefore the stone travels 800 meters if it falls for 12.76 seconds.