How Can an Astronaut Determine Falling Object Acceleration on the Moon?

[losolomd]

Homework Statement

You are an astronaut doing physics experiments on the moon. You are interested in the experimental relationship between distance fallen, y, and time elapsed, t, of falling objects dropped from rest. You have taken some data for a falling penny, which is represented in the table below.
(a) y (m) 10 20 30 40 50
(b) t (s) 3.5 5.2 6.0 7.3 7.9
You expect that a general relationship between distance y and time t is y = BtC, where B and C are constants to be determined experimentally. To accomplish this, create a log-log plot of the data.
(a) Graph log(y) vs. log(t), with log(y) the ordinate variable and log(t) the abscissa variable. (Do this on paper. Your instructor may ask you to turn in this work.)

(b) Show that if you take the log of each side of your expected relationship, you get log(y) = log(B) + C log(t). (Do this on paper. Your instructor may ask you to turn in this work.)

(c) By comparing this linear relationship to the graph of the data, estimate the values of B and C.
B = 1 m/s2
C = 2

(d) If you drop a penny, how long should it take to fall 1.0 m?
3 s

(e) In the next chapter, we will show that the expected relationship between y and t is y = ½at2, where a is the acceleration of the object. What is the acceleration of objects dropped on the moon?
4 m/s2

Homework Equations

y = BtC

The Attempt at a Solution

log(Y)+ log(t) = log(Y).(t)

 

[ehild]

That y=BtC should be y=B*t^C. Taking the logarithm of both sides it is log(y) = log(B) + C log(t). Plot the logarithm of height, log(y) as function of log(t). The point will scatter around a straight line. Either draw the line and read the slope and log(B) from the graph, or determine the constants with linear regression.

ehild

 

[losolomd]

Thanks for all your help..