An astronaut on PLANET OSKI is standing on a cliff of unknown height H. The astronaut would like to ascertain the gravitational acceleration g0 of PLANET OSKI. In order to determine H and g0, the astronaut performs two experiments:
1) FIrst she leans over the edge of the cliff and drops a rock. She notes that it takes approximately T1 = 2.0 s for the rock to land on the surface below.
2) Next, she leans over the edge of the cliff and tosses a second rock straight upwards. The rock rises for approximately h = 1.0 m, then falls to the ground below. A time T2 = 2.34 s elapses between the moment the rock leaves her hand and the moment the rock strikes the ground.
Find H and g0. (Assume that air resistance is negligible.)
1) vf2 = v02 + 2aΔx
2) vf = v0 + at
3) xf = x0 + v0t + ½(a)t2
4) Quadratic Formula
The Attempt at a Solution
I tried solving this three times. On the first and third tries, I failed to eliminate any variables. On the second try, I got g = 1.309 m/s and H = 2g, but this does not satisfy the astronaut's second experiment of being only 2.34 seconds long. Algebra problems with many variables like this are very time consuming and I don't have a good strategy for solving them. I spent two hours trying to tackle this problem! For this question, I would simply plug in as many known values as I am given into the equations. Then, I would start manipulating them while praying that I would somehow end up with an equation with only one variable. Is there a good strategy for this? All suggestions are welcome.