As an astronaut visiting the Planet X, you\'re assigned to measure the free-fall

Question

As an astronaut visiting the Planet X, you're assigned to measure the free-fall acceleration. Getting out your meter stick and stop watch, you time the fall of a heavy ball from several heights. Your data are as follows. Graphing either h versus t^2 or t^2 versus h gives a straight line. In the graph shown above, we chose to plot h on the vertical axis and t^2 on the horizontal axis because the theoretical kinematic equation gives position as a function of time. From the equation for the line of best fit given, calculate the free-fall acceleration on Planet X? Express your answer using two significant figures and appropriate units. g_x = 11 m/s^2

Explanation / Answer

We have the kinematic equation

s =ut + (1/2)at2

Where,

s - displacement (here, h)

u - initial velocity (here, u=0)

t- time

a - acceleration( here a= gx)

Then,

h = (1/2)gx t2

Therefore,

gx = 2h/t2

It is given, when h = 5 m, t = 1.17s

gx = 2x 5/ 1.172 = 7.305 m/s2

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