Calculating the Height of a Cliff Using Rocks

[koolbaseman]

This problem doesn't have a diagram or a picture so:


Suppose you land your spacecraft on a distant planet and disembark extremely close to the top-edge of a cliff. The planet's acceleration due to gravity is unknown and you want to know the height of the cliff. Utilizing your accurate watch you let a rock fall from rest off the cliff edge and note it takes 13.00 seconds to impact the ground below. Next, you throw up a second rock (from the cliff's edge) and it rises to a height of 3.000 meters. The total time (from release to impact) for the second rock to reach the ground is 13.50 seconds. Calculate the height of the cliff.


Thanks for any help!

 

[Snazzy]

If it doesn't have a diagram or picture, then make a diagram or picture. You know your initial velocity, and the time it takes to fall to the bottom of the cliff in the first scenario. You don't know height or acceleration.

In the second scenario, you know that at the top of the upward throw, the velocity is going to be 0, and it takes 13.50 seconds to fall 3 + h metres. Again, you don't know the height or the acceleration.

Two equations, two unknowns.

 

[Moetasim]

I would approach this problem by first identifying the known variables and equations that can be used to solve for the unknown variable, which in this case is the height of the cliff. The known variables are the time it takes for the rock to fall (13.00 seconds), the height the rock reaches when thrown (3.000 meters), and the total time it takes for the rock to reach the ground (13.50 seconds).

To solve for the height of the cliff, we can use the equation h = 1/2 * g * t^2, where h is the height, g is the acceleration due to gravity, and t is the time. We have two sets of data, one for the falling rock and one for the thrown rock, so we can set up two equations and solve them simultaneously to find the value of g.

For the falling rock, the equation would be h = 1/2 * g * (13.00 seconds)^2, and for the thrown rock, the equation would be h = 3.000 meters + 1/2 * g * (13.50 seconds)^2.

By setting these two equations equal to each other, we can solve for g and then use that value to calculate the height of the cliff.

Once we have the value of g, we can plug it back into either equation and solve for h. The final answer will be the height of the cliff in meters.

It's important to note that this calculation assumes that the acceleration due to gravity on this distant planet is constant and equal to the value of g we calculated. If the planet's gravity is not constant, then this calculation may not be accurate. In that case, we would need to gather more data and potentially use more advanced equations to accurately calculate the height of the cliff.