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 = 1/2gplanett2, 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 0.100 s2/m. Based on your data, what is the value of gplanet?

Explanation / Answer

given

y - y0 = 0.5*gplanet*t2 (1)

also given slope

t2/(y-y0) = 0.100 s^2/m

(y-y0)/t2 = 1/0.100 = 10 m/sec^2 (2)

10 = 0.5*gplanet

gplanet = 10*2 = 20 m/sec^2

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