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.