[williamh26]

An astronaut has crash landed on a planet that little is known about (not even the acceleration due to gravity). She must descend a steeo cliff to find shelter, but wants to know how high the cliff is before making the attempts. She happens to have salvaged a stopwatch from the wreckage, and uses this to make two experiments. First releases a rock from the very edge of the cliff, and finds that 2.58 seconds elapse before the rock reaches the bottom. Then stands up and releases another rock, this time from apposition level with the top of her head, which she knows is 2.00 meters above the top of the cliff. This stone requires 2.64 seconds to reach the bottom of the cliff.

a. how high is the cliff?
b. what is the acceleration due to gravity on the surface of the planet?
c. Draw a graph of the given situation.

[ebaines]

If h = height of the cliff, then using x = 1/2 a t^2 you have two equations describing the experiment:

h = 1/2 g (2.58s)^2
h+2m = 1/2 g (2.64s)^2

Subtract the first equation from the second and solve for g.