You are exploring a planet and drop a small rock from the edge of a cliff. In co

Question

You are exploring a planet and drop a small rock from the edge of a cliff. In coordinates where the +y direction is downward and neglecting air resistance, the vertical displacement of an object released from rest is given by y y0 = 1 2 gplanett2, where gplanet is the acceleration due to gravity on the planet. You measure t in seconds for several values of y y0 in meters and plot your data with t2 on the vertical axis and y y0 on the horizontal axis. Your data is fit closely by a straight line that has slope 0.800 s2/m. Based on your data, what is the value of gplanet?

Explanation / Answer

The problem can be solved as follows:

You are simply measuring d and t for an object falling from rest.

Fitting the data to the equation d = ½at² (vi = 0)

t² = 2d/a .. compared with linear equation form y = mx + c ..
y t²
x d
gradient m 2/a
c = 0

m = 2/g = 0.80 m/s²

=> g = 2/0.80 => g = 2.50 m/s²

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