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

where gplanet is the acceleration due to gravity on the planet. You measure t in seconds for several values of

in meters and plot your data with t2 on the vertical axis and

on the horizontal axis. Your data is fit closely by a straight line that has slope 0.400 s2/m. Based on your data, what is the value of gplanet?

Explanation / Answer

as y=y0 -1/2 g t^2.This equation is basic kinematic equtaion for a body in uniform acceleration.
You will plot this curve.
Slope of the curve y = mx +c is m.
with x as horizontal axis and y as vertical axis.
By comparing these two equations you get the slope as 2/g.

according to your plot 2/g =0.4

so g=5 m/s^2

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